Drag Coefficients for Flat Plates, Spheres, and Cylinders

DRAG COEFFICIENTS FOR FLAT PLATES SPHERES AND CYLINDERS MOVING AT LOW REYNOLDS

NUMBERS IN A VISCOUS FLUID

by

ALVA MERLE JONES

A THESIS

submittelti to

OREGON STATE COLLEGE

in partial fulfillment of the requirements for the

degree of

MASTER OF SCIENCE

June 1958

APFROVED T

Redacted for Privacy

In 0hrrg of laJar




Drtc tbrclr la prrrontr a h4ul^r-J-trlqql

lfypcd by ftrcdeetr Or Joncr

i

ACKNOWLEDGEMLNT

The author wishes to express his appreciation to

Dr J G Knudsen for helping with this investigation and

to the Do Chemical Company for aiding this work through

a Research Fellowship

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ii

TABLE OF CONTENTS

Pa ge

Introductionbullbullbullbullbullbull bull 1

Analysis of Theoretical Solutions and

Obtaining Drag Coefficient by

Review of Literature 3

Theoretical Po ssibilities 3

Experimenta l Databullbullbullbullbullbull bull bull 11

Experimental Data bull bull bull bull bull bull bull bull bull bull 12

Literature Containing General Theory bull 14

Theoretical Considerations 16

Definition of the Dra g Coefficient 16

Dimensional Analysis bull bull bull bull bull bull bull bull bull 19

Exact Solutions for Dra g Coefficient bull 21

Moving Bodies and Moving Fluid bull bull

Description of Apparatus bullbullbullbullbull bull

Force Measuring Equipment bull bull bull bull

Spheres Cylinders and Plates

Experimental Procedure bullbullbullbullbullbullbull bull bull

Viscosity and Density Cal ibration 35

Velocity Measurements bull bull bull bull bull bull

Foree Measurements

Experimental Results bull bull bull bull bull bull bull bull bull bull bull 37

25

26

26

30

35

35

36

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TA BLE OF CONTfN lS (CONT )

Page

Discussion of Results bullbullbullbull bull 48

Correction and Accuracy of

Comparison of Results with Other Data

Appendix bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull

Measurements bullbullbullbullbullbullbullbull 48

Analysis of Results bull bull bull bull bull bull bull bull bull bull 50

and Theoretical Solutions bull bull bull bull bull bull bull 53

Summary and Conclusions bull bull bull bull bull bull bull bull bull bull 57

Nomenclature 60

Biblio graphy bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 62

Experimental Data bull bull bull bull bull bull bull bull bull bull bull 64

Density and Viscosity Calibration bull bull bull 89

Sample Calculations bull 92



iv

LIST OF I LLUSTRATI OS

Fi gure Page

1 Drag Coefficients for Spheres bullbullbullbull 5

2 Drag Coefficients for Cylinders bullbullbull 6

Dra g Coefficients for Flat Plates shyParallel Flow bullbullbullbullbullbullbullbullbullbullbullbull 8

4 Drag Coefficients for Fl a t Plate s shyPerpendicular Flow bull bull bull bull bull bull bull bull bull

5 Block Diagram of Apparatus bull bull bull bull bull 27

6 Apparatus - Left View bull bull bull bull bull bull bull 28

7 Apparatus - Ri gh t View 29

8 Photograph of Spheres Cylinders and Plates bull bull bull bull bull bull bull bull bull bull bull bull bull 33

9 Drag Force on the Wires - Li gh t Oil 38

10 Dra g Force on the Wires - Heavy Oil 39

11 Data for Spheres bull 40

12 Data for Cylinders - LD 16 24 32 bull bull bull bull bull bull bull bull bull bull bull bull bull 41

13 Data for Cylinders shyLD c 2 and 4 bull bull bull bull bull bull bull bull bull bull bull 42

14 Data for Cylinders shyLD 6 8 and 12 bull bull bull bull bull bull bull bull bull bull 43

15 Data for Fl a t Plates - Parallel Flow 45

16 Data for Flat Plates - Perpendicular Flow - WL 2 bull bull bull bull bull bull bull bull bull bull bull 46




v

LIST OF IILUSTRI TIONS ( CONT )

Figure Page

17 Data for Flat Plates - Perpendicular Flow - WL 1 4 47

18 Dependence of Viscosity Ol lempera ture - Li ght Oil 90

19 Dependence of Viscosity on l1empera ture - Heavy Oil 91

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vi

LIST OF TA BLES

Table Pa ge

I Description of the Sphere s Cylinders and Plates bullbullbullbull 31

II Data for Spheres bull 64

III Data for Cylinders bull 67

IV Data for Flat Pla tes - Para l lel Flow bull bull bull bull bull bull bull bull bull bull bull bull bull bull bull 77

v Data f or Fl a t Plates shy

VI Dependence of Density on

Perpendicular Flow bull bull 82

Temperaturebullbullbullbullbullbullbullbullbullbullbullbull 89


~UMBERS I N A VISCOUS F LUID

LJTRODUCTI ON

The study of laminar flow of very viscous fluids over

immersed bodies is important in many engineering problems

In the field of aerodynamics the study is becoming inshy

creasingly important because as the speed of aircraft inshy

creases there is a tendency for the occurrence of a re gion

of laminar flow on their surfaces due to the low density

of the air at the hi gh speeds Furthermore the mainte shy

nance of extensive laminar flow is desirable in order to

minimize the friction dra g Other problems include the

theory of lubrication and the flow over banks of tubes in

heat exchangers Many of the polymers formed in the field

of plastics are highly viscous materials and problems

such as the power requirement for mixers are encountered

in flow over immersed bodies at low Reynolds numbers

At present there are only a few theoretical solutions

and approximations and almost no experimental data on flo

over spheres cylinders and flat plates in the range of

Reynolds numbers from 0 01 to 10

The force of resistance is related to the reometry of

the immersed body and the properties of the fluid by

2

a non-dimensional drag coefficient which is defined by the

followin g equation

1)

The drag coefficient is also a function of the Reynolds

number for geometrically similar bodies Thus if the

drag coefficient and the Reynolds number are known the

force of resistance for flow over immersed bodies or

bodies moving in a fluid can be predicated

The present investi ga tion involved a determinati n of

the drag coefficient as a function of the Reynolds number

and geometric ratio for spheres cylinders and flat plates

at Reynolds numbers rangin g from 0 01 to 10 The drag

coefficients were determined by measuring the force of re shy

sistanco and calculating the drag coefficient by the use of

Equation (1) For each dra g coefficient a Reynolds number

las calculated From a plot of the data it was possible to

determine an e xpression relating dra g coefficients Reynolds

numbers and LD and WL The data and empirical equations

have been compared to other available data and theoretical

solutions

3

REVIEW OF LITERATURE

Theoretical Solutions

A large number of investigators have analyzed laminar

flow of a viscous fluid past various immersed bodies

Their analyses have resulted in expressions for dra g coef

ficients and boundary layer velocity profiles In their

work they have made various assumptions which ac count for

fairly wide discrepancies bet een the results of individual

investigators In addition li ttle experimental data are

available to compare with theoretical work

Stokes (14 p 55) was one of the first investigators

to study the motion of a veryvfscous fluid over an immersed

body In 1850 he published the well-known solution for the

motion of a sphere whereby the force of resistance is

given by the following equation

F 6ffA vr (2)

bull By substituting the definition given in Equation (1) the

drag coefficient for fluid flowing past a sphere at low

Reyno l ds numbers is

fd - 24-re (3)

bull Equation (3) holds for Reynolds numbers up to nearly 1 0

Oseen (11 p 122) improved Stokes analysis

4

by linearizing the Naviermiddot Stokes equations The dra g coefshy

ficient of the sphere by Oseen s analysis is

f - 24 1d - Re (1 r 3Re) (4) I6

Equation (4) is good for Reynolds numbers u p to 5 Vfuile

Oseens work was published in 1910 his method of

linearizing the equations of flow has been used by recent -investi gators in studying the flow of fluids over elliptic

cylinders and flat plates

Horace Lamb (8 p 112-121) as another early conshy

tributor td the study of the flow of viscous fluids over

immersed bodies He presented a simpler demonstration of

Oseen s results and further developed their scope and

significance Also he a pplied the same method to flow

past a circular cylinder Lambs solution for the dra g

coefficient of circular cylinders is

f - 8 ff (5) d - Re (2002 - ln Re)

Equation (5) is good only for Reynolds numbers up to 0 5

Bairstow Cave and Lang (2 p 383- 432) extended

Lamb s solution to eover lar ~er values of Reynolds numbers

Their solution is plotted in Fi5~re 2

Goldstein (3 p 225bull235) has solve d Oseens equations

completely for fluid flow at small Reynolds numbers past

spheres His solution take s into account the hi gher

5

I 00

50

2

10

I I

i I

middoti

- -middot middot- ~ L ~ middot _ ltmiddot --middot-~ i -- --

STOKES OSEEN LIEBSTER 0 0 GOLDSTEIN-middot-middot-

It

I

I

--

i

-

~-+~~-+--+~~H- ~~--~ -4~+ ~- ~middot middot~middot ~middot ~-_~HH I middot1-_middot

11 ~ ~ - I bull J

bullmiddotmiddotbull -tf-

I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re

DRAG COEFFICIENTS FOR SPHERES

Fl GURE I

1

6

a-

rr

- ~middot

e

bull bull WIESELSBERGER o o INAI --LAMB bull bull ALLEN a SOUTHWELL - middot - TONOTIKA a AOI - middot shy BAIRSTOWCAVI a

LAN I

--middot

J middot bull bull

-=

bull JIo

I l---_-_+-~__-+--_~-+-+-+-l-+-+-+--+-+--H-shy--tshy---i-7--+-+---t---t--tlshybullmiddotmiddot t-t--t-t--r-t--rt bull 1 I ~--- --shy

r 1 tt1j iffilfl if rtC =~ middotshyh tn ~ ~ r~ wrw~ ~ ~ u middot ~~ 1~ middot~-t middotbullmiddotbull tl= t fsect s ~

1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1

Rt DRAG COEFFICIENTS FOR CYLINDERS

FIGURE 2

7

powered terms in the series solution that were omitted by

Oseen The solution is plotted in Figure 1 It covers

values of Reynolds numbers up to 10

In recent years several people have developed approxi shy

mate solutions of drag coefficients for flow at a low

Reyno l ds number over ell iptic cylinders for various ratios

of major and minor axes and angles of incidence For the

major axis equal to the minor axis the result is a circushy

lar cylinder For a ratio of major axis to minor axis of

infinity the resul t is a flat plate with parallel flow

for a zero anglo of incidence and a f l at plate ith perpenshy

dicular flow for an angle of incidence of ninety degrees

Tomotika and Aoi (15 p 290-312) have obtained e xact

ntJm3rical solutions of Oseen s equations for steady flo

past an elliptic cylinder in terms of elliptic coordinates

When the calculations are based upon Oseens equations

they found that the total drag can be analyzed into pressure

and friction drag proportional to the axes of the cylinder

for any Reynolds number Their solutions are plotted in

Figures 2 3 and 4 and cover Reynolds numbers from 0 4 to

4 0

Imai (4 p 141- 160) has presented a numerical solution

to flow past an inclined elliptic cylinder for Reynolds

numbers of 0 1 and 1 0 His method is essentially one of

5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I

I I middotmiddot T p

o o INAI - JANSSEN

bullbull bullbullbull TONOTIKA a AOI

~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1

DRAG COEFFICIENTS FOR FLAT PLATES PARALLEL FLOW

FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot

- middot-- ~-f--l -middot

I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-

DRAG COEFFICIENTS FOR FLAT PLATES

PERPENDICULAR FLOW

FIGURE 4

10

successive approximations in poter series of Reynolds

numbers The solution is shown in Figures 2 3 and 4

Allen and Southwell (1 p 129-145 ) have used the

relaxation methods to determine the motion of a viscous

fluid past a fixe d circular cylinder Their solution covers

Reyno l ds numbers from 01 to 10 and is plotted in Figure 2

Blasius (7 p 66) investigated the laminar flow in

the boundary layer of a thin flat plate immersed in a stream

flowing parallel to the surface of the plate By making

several assumptions he obtained an exact solution of the

simplified flow equations

One of the most recent developments in the study of

flow over immersed bodies at low Reyno l ds numbers is that

t y Janssen (6 P bull 173-183) who used an analog computer to

determine drag coefficients for flat plates in parallel

flow By defining vorticity ( lt ) as

o1 d v_ J u (6)d X d Y

and the stream function ( tf as

u = d~ v = Jtf (7) d y d X

where u is the velocity in the direction of the x - cobull

ordinate and v is the velocity in the direction of the y shy

coordinate and making the proper substitution in the

Navier-Stokes equation he obtained the following two

11

equations Vlo(_ bull _1 [- d ltf d( ~ ~ d(]

J dX dJ Jj dX (8)

--lt ( 9 )

These equations have the form of the Poisson equation and

were solved by means of two resistance net orks His soshy

lution covers the range of Reynolds numbers from 0 1 to 10

and is plotted in Figure 3

A large amount of work has been done by other investishy

gators for flow over flat plates but their ~ork does not

cover Reynolds numbers of less than 10

Experimental Data

Very little experimental data has been obtained for

drag coefficients of flat plates cylinders and spheres in

the range of Reynolds numbers from 01 to 10

There is no data for flat plates in perpendicular flow

Janour (5 p 1-40) obtained drag coefficients for parallel

flow over flat plates However his data only covers

Reynolds numbers down to twelve which is above the range

being considered in the present work One significant

result of Janours work is establishing a lo~er limit for

the well-known Blasius formula

fd 1328 12 (10)(Re )

12

4of about 2 0 X 10 bull The equation proposed by Janour for

Reynolds numbers of 12 to 2335 is

2 90fd (He) 601 11)

Drag coefficients for flow over cylinders have been

experimentally determined by Wieselsberger (16 p 22)

His data covers Reyno lds numbers from 4 to 100 The data

for very long cylinders is plotted in Fi poundUre 2 VJieselsshy

berger also studied the effect of the length ~to-diameter

ratio on drag coefficients He found that the drag coefshy

ficient decreases with a decreasing LD r a tio at a constant

Reynolds number However his data for LD other than

infinity was obtained at Reynolds numbers above 40

Relf (13 p 47-51) measured the resistance of flow

over cylinders but only for Reynolds numbers above ten

Liebster ( 9 p 541-562) measured the resistance of

flow over spheres His data cove r s the range of Reyno lds

numbers from 0 13 to 101 His data is plotted in Fi poundure 1

Analysis of Theoretical Solutions and Experimental Data

The data of Liebster (9 p 548) provides a good check

for the solutions of Stokes (14 p 55) Oaeen 11 p 122)

and Goldstein (3 p 234) for flow over spheres at Reynolds

numbers less than 05 As Figure 1 shows the results are

13

in good agreement in that range As the Reynolds number

becomes grea ter than 1 0 it is known that Stokes formula

does not hold true The results of the other workers are

very close up to a Reyno l ds number of 2 so that all of

their data is probably very good in that range Above a

Reynolds number of 3 Oseenta solution is proba bl y not very

go od since it was only an approximation At a Reynolds

number of 10 Liebsters data is about 25~ lower than

Goldsteins solution so the true solution is probably

somelhere between the two values

Since Lambs solution (8 p 112-121) for flow over

a cylinder was based upon the method of Oseen his solution

is probably very go od for Reyno l ds numbers of less than 1

The solutions of Tomotika and Aoi (15 p 302) Imai

(4 p 157 ) and Bairstow Cave and Lang (2 p 404) seem

to substantiate this fact since they all agree with each

other as shown in Figure 2 The only solution which does

not agree is that _of Allen and Southwell (1 p 141)

For the range of Reynolds numbers from 1 to 10 the

different results vary considerably Lambs solution is

not correct The results of lomotika and Aoi and Bairstow

Cave and Lang as shown in Figure 2 are very close Howshy

ever the data of Wieselsberger (16 p 22) the only

experimental work for cylinders is 30t below the results

14

of t he other workers It is interesting to note that the

solution of Allen and Southwell coincides with Wiese lsshy

bergers data in this ran ge

Very little ~ork has been done for flow at low

velocities over f l at plates both paralle l and perpenbull

dicular to the flowing stream For parallel f low at very

low Reyno l ds numbers the solutions of Imai (4 p 157)

Tomotika and Aoi (15 bull P bull 302 ) and Janssen (6 p 183 ) are

very close as shown in Figure 3 For Reynolds numbers

near 10 Janssens solution is below that of Tomotika and

Aoi

For flat plates perpendicular to flow there is only

the theoretical data of Tomotika and Aoi (15 p 302 ) and

I mai (4 p 157) Their solutions as before nearl y

coincide

Litera ture Containing General Theorx

Several excellent books and monographs containing the

general theory of flow over immersed bodies particul arly

at low Reynolds numbers are available

Knudsen and Katz (7 P bull 64 105 ) give a good discussion

of flow turbulent and laminar pas t thin flat plates

circular and elliptical cylinders and spheres Boundaryshy

l ayer theory and boundary-layer equations are included

15

The Blasius solution is described in detail There is a

section on drag coefficients with many graphs of different

data However most of these do not cover low Reynolds

numbers

Severa l chapters of the book by Pai (11 P bull 100- 260)

pertain to drag at low Reyno l ds numbers In addition to

the fundamenta l equations of f luid dynamics there is

excellent material covering the Navier-Stokes differential

equations theory of very slow motion and the boundaryshy

layer equations His description of the Oseen method of

linearization (11 p 122) is particularly good

Prandtl (12 p 98-196) has several good sections on

flow past immersed bodies Among these are the sections on

the motion of bodies in viscous fluids (12 p 105-110)

and the resistance of bodies immersed in fluid (12 p 174shy

178 ) There is also a section containing the experimenta l

results of fluid resistance Included is drag coefficient

data for spheres cylinders and plates at all Reynolds

numbers

Though short Janour 5 p 1-40) has a good discussion

of the general theory of the resistance of bodies in l aminar

flow

16

THEORETIC f L CONSITERATI 01TS

Definition of the Drag Coefficient

The resistance or dra g of a body movin g in a liquid

or gas or exposed to a medium flowin g past it is a compli shy

cated function of the geometric properties of the body and

physical properties of the medium The resistance depends

upon the size of the body geometric shape and position

quality of surface a nd the velocity viscosity and de nsity

of the medium

Newton postulated that the resistance with which a

fluid opposes the motion of a body immersed in it through

the force of its inertia must be proportional to the area

of the section of the body at ri ght angles to the direction

of flow and also proportional to the density of the fluid

and to the square of its velocity This result may be

explained by the followin g simple ar~nnent (12 p 174)

In a unit of time the body must move a mass of flui d

m f av (12)

out of its way and in doing so imparts a velocity to each

element of the fluid This velocity is proportional to

the velocity of the body The resistance is equal to the

momentum imparted to the fluid and is therefore proportional

to

17

mv p av 2

(13 )

where a is the projected area of the body on a plane

normal to the direction of flow

In Newton s theory the laws of collision of elastic

bodies are applied to the resistance of a fluid Jewton

regarded the medium as consisting of particles fre e to move

but at rest which are regularly reflected by the moving

body The detailed results however have proved unsound

The Newt onian concept of fluid resistance has been

replaced by the hydrodynamica l theory hereby the reshy

sistance consists of the pressure differences and friction

stresses arising from the fluid flo ing around the body

These resistances are sometime~ referred to as form drag

and surface drag A fundamental difference between the old

and new theories is that in the former only the shape of ~

front portion is considered whereas it is known that the

phenomena giving rise to resistances are largely due to the

shape of the rear portion

In general the pressure differences predominate and

may be taken as proportiona l to the dynamic pressure

corresponding to the velocity that is as proportional to 212 f v bull The resistance being the product of pressure

differences and the area exposed to it is proportional to

12 f av2 bull

18

There are several methods of defining the drag coefshy

ficient In Germany the United Statea and most countries

the drag coefficient is defined as

where F - force of resistance

= density of the fluid~ ap - projected area-

v velocity and

fd - drag coefficient -This is the definition used in the present work

In soma countries particul arly England the drag

coefficient is defined as

14 )

where the symbols are the same as defined in Equation (1)

The data of Tomotika and Aoi (15 p 302) Goldstein

(3 Pbull 234) and Bairstow Cave and Lang (2 p 404)

based upon Equation (14) has been changed so that it is

defined as in Equation (1) and can be compared easily with

that of other investigators

For the flat plates in paralle l flow the dra g coefshy

ficient is defined as

19

F 12 f f aw v 2

(15)go

where F and v are the same as in Equation (1) and

aw wetted area

Some investigators define the drag coefficient as

follows 2

F 12 fd f b v (16) go

where F force of resistance par unit width and

b a characteristic dimension such as diameter for

cylinder and length for a flat plate

It is easily seen that when Equa tion (16) is multiplied by

the width it reduces to Equation (1) for cylinde r s and

flat plates in perpendicular flow Also Equation (16)

when mul tiplied by the width reduces to Equation (15) for

the case of flat pl ates in parallel flo 1f only one side

of the plate is being considered

Obtaining Drag Coefficient by Dimensional Anal ysis

The drag coefficient may also be obtained by dishy

mensional analysis There are several methods for getting

dimensionless groups butthe meth od used here is the r

20

Theorem described by McAdams (10 p 30)

The factors involved are b v f F ~ and g bull It is0

necessary to include gc since both mass and force terms

are involved If the dimensions are solved in terms of

the dimensionally incompatible factors the following is

obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )

Each of the remaining factors g0 ~ ) must produce a

dimensionless group when its dimensions are eliminated by

one or more of tho above four equations

Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le

Equations 21) and (22 ) yield the following dimensionless

groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)

If a is substituted for b2 and 12 f v2 for f v2 then

Equation 23) is the same as Equation (1) Also one

dimensionless group may be expressed as a function of

another so that

f cent (Re) bull (25)d

Thus drag coefficients for constant Reyno lds numbers and

ge ome tric similarity have the same value

Dimensional analysis lacks the pictoral quality of

dynamic similarity considerations but it has the adshy

vantages of not using the knowledge of the equations

governing the problem

Exact Solutions for Drag Coefficient

The possibilities of an exact theoretical solution of

the laminar steady flow about bodies and the calculation

of the resistance are examined

The laminar motion of a viscous fluid is governec by

the Na vier-Stole s equations which for two - dimensional

incompressible flow in the absence of external forces are

- g (26 ) =c f

and

22

27)

where x and y distances in the coordinate direct1oqs

u and v velocities in the x and y directions

respectvely

t bull time

p static pressure and

2 1 Laplacian opera tor

For the case of steady flow the terms Ju and dv are Jt Jt

zero The Na vier-Stokes equations are supplemented by the

equation of continuity which for an incompressible fluid is

J u f J v 0 (28 )Jx n

Pal (11 p 37) gives a good derivation of Equations (26)

and (27) The following boundary conditions may be applied

(1) As x approaches I and y approaches I cP the - -veloc ity equals a constant and

(2) At the wall the middot normal and tangential components

of the velocity v nish

A solution to the Navier-Stokea equations would give u v

and the pressure distribution The drag force could be

calculated from these unknown quantities The equations

are non-linear and their general solution is unknovm

23 because a superposition of particular sol utions is

impossible Howeve r solut ions can be obtained if the

equations are simplified

If viscosity is assumed zero the Euler equa t ions of

motion for an ideal f luid

du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)

are obtained The inte gral of these equations a long a

streamline gi ves t he Bernoulli equation which expresses

the law of the conservation of energy A streamline is

tangent to the velocity vector at every poin t

For the case of steady flow Blasius assumed that the

thickness of the boundary layer is small J2 u is less than

I JYZ2d u and that v is less than u With the s e assumptions the r-y following equation is obtained

d u f ) u (31)urx VTY

Equation (3l)t along with the continuity equation

completely describes the flow in the laminar layer Blasius

obtained an exact solution of these equations

The non-linearity of the Navier-Stoke s equations lies

in the terms on the left side of the equations If these

24

terms are neglected the equations simplify to

(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull

The solutions of these equations for flow about a sphere

was derived by Stokes (14 P - 55) Equations (32) and (33)

are good only at very low Reynolds numbers when the viscous

forces are large compared to the omitted inertia forces

Oseen improved upon the Stokes solution by replacing

the inertia terms u du v du u d v and v dv by the rx JY rx 7Y approximate terms u d u v Ju u J v and v dv

o rx o e y o rx o d Y

where u and v are the constant value of the velocity0 0

components u and vat an infinite distance from the body

Near the body where the values of u deviate from u the 0

inertia terms are small compared with the viscosity terms

so that the Oseen equation becomes the Stokes equation

Thus for very low Reynolds numbers high viscosity or

small dimensions neglecting the inertia forces will give a

good solution to the Navier-stokes equations of flow In

all cases this t ype of flow has the property that the

resistance to motion is proportional to the velocity which

25

means that the drag coefficient must be inversely probull

portional to the Reynolds number

Moving Sodies and Moving Fluid

The question arises as to how the resistance of a

body moving in fluid at rest is related to the force

exerted by a moving fluid on a body at rest Prandtl

(12 p 179) explains that as long as the fluid is moving

perfectly uniformly there is no difference between the two

cases The superposition of a common uniform motion (equal

and opposite to the velocity of the body so that the latter

is brought to rest) makes no difference to mechanical

phenomena If flo is not perfectly uniform with respect

to the body or if the flow is turbulent the resistances

are usually greater for a moving fluid on a body than for

a body moving through a fluid

26

DESCRIPTI ON OF APPARATUS

Force Measuring Equipment

The force measuring equipment was connected as shown

in the diagram in Figure 5 Figures 6 and 7 are photobull

graphs of the apparatus

The apparatus is constructed to move various bodies

vertically through a viscous fluid It consisted of a

16 horsepower motor coupled to a Revco speed reducer A

four-step V-pulley with diameters of 34 1-14 l-34 and

2-l4 inches was installed on the speed reducer The drag

force as measured by means of a 2-pound spring scale with

12 ounce divisions purchased from Scientific Supply

Company This scale was calibrated on a platform scale

measuring to the nearest 0 001 pound It was connected to

the four step pulley by means of a nylon cord A capstan

arrangement with a single turn around the pulley as used

to connect the scale to t he pulley A wei ght was placed

as shown in Fi gure 5 at the end of the cord Several

different wei ghts were used in order to counterbalance the

varying wei ghts of the cylinders and spheres With this

arrangement a wider range of velocities was obtained

A fine wire 0 003 inch diameter was used to connect

27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I

L------ COOL lNG WbullTERWATER ACKET

INLET

BLOCK DIAGRAM OF APPARATUS

FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29

APPARATUS- RIGHT VIEW

FIGURE 7

30

the plates cylinders and spheres to the scale

Fifteen gallon oil drums set inside of a 31 gallon

barrel we~e used for performing the experiment The oil

drum was set upon a bracket inside the barrel so that coolshy

ing water could be circulated all around the oil except for

the top

Two types of heavy duty gea r oil were used Shell

SAE 140 and Richfield SAE 250 Viscosities of the two oils

are shown in Figures 18 and 19 and densities in Table VI


The objects for which drag measurements were obtained

are described in Table I Figure 8 wi th two exceptions

is a photograph of the spheres cylinders and plates

studied in th~ experiment A 1-12 and a 2 inch sphere

were substituted for the 14 and 12 inch spheres since

the small spheres were too small to register a force on the

scale Also the 1 x 2 plate for perpendicular flow is

not shown

Holes were drilled in the spheres and the ends of the

cylinders Ordinary household cemen t was used to connect

the 0 003 inch diameter wire to the objects Small holes

were drilled in the corner of the plates and the wires were

tied to the plates For the plates in parallel flow three

31

TA BLE I

Description of t he Spheres Cylinders and Plates

sehe re s

No D-in Material

1 34 stee l 2 1 steel 3 1 12 steel 4 2 steel

Cylinders

No L-in D-in Material-1 2 14 steel 2 2 12 steel 3 2 1 steel 4 2 1 12 aluminum 5 4 14 steel 6 4 12 steel 7 4 1 steel 8 4 1 12 aluminum 9 6 14 steel

10 6 12 steel 11 6 1 steel 12 6 1 12 aluminum 13 8 14 steel 14 8 12 steel 15 8 1 steel 16 8 1 12 aluminum

Flat Plates - Parallel Flow

No Wbullin L-in Th-in Material-la 4 1 364 steel lb 1 4 364 steel 2a 4 2 364 steel 2b 2 4 364 steel 3 4 4 364 steel 4a 4 8 364 steel 4b 8 4 364 steel

32

Flat Plates - Per12endicular Flow

W-in L-in Th-in Material2 1 8 2 764 aluminum 2 5 1 12 764 aluminum 3 4 1 364 steel 4 2 12 364 steel 5 8 4 764 aluminum 6 6 3 364 steel 7 4 2 3 64 steel 8 2 1 364 steel 9 4 4 3 64 steel

10 3 3 364 steel 11 2 2 364 stee l 12 1 1 364 steel

-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~

FIGURE e- PHOTOGRAPH OF SPHERES CYLINDERS AND PLATES

34

holes were drilled so that each plate could be used for

two geometric ratios by changing the wires (See for

example plates la and lb in Table I

35

EXPERI MENTA L PROCEDURE

Viscosity and Density Calibration

A calibrated hydrometer measuring to the nearest

0002 was used to measure the density Table VI shows that

the effect of temperature on density is practically negli shy

gible in the small temperature range used

A Brookfield Synchro-lectric viscometer was used to

measure the viscosity of both the light and heavy oil

Figures 18 and 19 show the effect of temperature on visshy

cosity In addition the viscosity of the light oil was

checke d using the falling ball method and the equation

D2--ltA (f s bull fl) g (34) l 8v

The viscometer was calibrated by the National Bureau of bull

Standards and was accurate to l tb

Velocity Measurements

The velocity of movement through the oil was measured

by determining the rate of rotation of the pulleys with a

stop watch Usually the time for 10 revolutions was

measured at the highe r ve locities and for 5 revolutions at

the low velocities From this information and the di

amaters of the pulleys the velocities ere calculated

36

The time was measured to the nearest tenth of a second

Since the measured time was usually between 20 and 40

aeconds 1 the error in ~easuring velocity was considered to

be less tha~ 0 5~

force Measurements

The object connected to the scale 1 was dropped to the

bottom of the oil drum The motor was started and the scale

was read as the object vms being pulled towards the top of

the drum Two or three readings were taken for each object

at each velocity In nearly all cases these readings were

the same

37

ti XPER I MENTAL RE STJLTS

The dra g coefficient and the Reynolds number were

calculated by the use of Equations (l or (15) for each of

the spheres cylinders and plates from the measured

quantities of force and velocity a~d the values of the vis shy

cosity and density corresponding to the temperature of the

oil It was necessary to ~ubtract from the measured force

the force on the wire The corrected force measurement was

then used to determine the drag coefficient The force on

the wire has been determined as being proportional to the

velocity A correction curve relating force on the wire

and ve l ocity is plo tted in Figure 9 for the li ght oil and

Fi gure 10 for the heavy oil

The calculated drag coefficients Reynolds numbers

and velocities along with the measured force for the spheres

cylinders flat plates - parallel flow and flat plates shy

perpendicular flow have been tabulated in Tables II III

I V and v respectively

The calculated drag coefficients have been plotted as

a function of the Reynolds number on logarithic graph paper

with geometric ratios as a parameter

Drag coefficients for the spheres are plo tted in

Figure 11 The data for the cylinders are plotted in

CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC

DRAG FORCE ON THE WIRE-LIGHT OIL

FIGURE 9

I -shy I -middot -- -shy -1shy _i-i I --~ I I _ -middotshy I i

_I_ - _ middot- LL I l l tmiddot - middot1middot ~- - - - -+i middotshy I - --+-cl - l

1 1 I I IV jc---- --r--middotmiddottmiddot r-middotmiddot--tmiddotmiddot---shy _____ _L __ --~- --1shy middotmiddotr-r-middott- 1 -f-f-T- _~ +-L--1---~- 1--l

~- - shy I-+---Rmiddot-- I I I l i ~~ i -~~ ~- -T f i rshy ~-- --shy i- ----~-- shy - middot1 shy

I i I i I I 1--- -middot - fshy middot i----1---+-shy - i-middot -~+-- --~- --~-- ---- -t+ I v-~~ -middot j

i I middot 1_ _ I tmiddot---+-+1-+--li~+middot -+--+-+-1-+-+-+-+--tc--1-+-t-11-shy - middot --t- 1---t- t----tmiddotshy --~-- -middot i-shy I 1i - ~ i I i v i middotmiddotmiddot

[~v +L~ + ~ - I~~j-+ r V I ~t--- -~-- I +---~-- I f-middot ---1-- ~ -- --- ) Li --+--+--+-+-+-+--1--+--+---t---4 -1--1--+-+--+-l-i

tl~ I I Q Y +l~~ii-+-++++-middotHH-++-+-+-+--H--++ -i t Imiddot i i 1 j _V I f1 r-t~-middot l--r-tshy -~ 7 middot 1 -shy middot middotmiddot I

DRAG FORCE ON THE WIRE- HEAVY OIL

FIGURE 10

40

+shy l i~ltgt ~ bull r-rshy I i t _l

1 lf-1-1 l+r+ fJ-Ct I+ t li 1~t rtH r+l rf-l It llil I I

l l~pound 11 1 ~middot ~~middott ~ It lqf L

t I+--= ~r 17 -Er I _ ~ _pound~- sect Imiddot I+

iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1

plusmn~ kplusmni - -STOKE S EQ

(~ l h+middot

ru HmiddotHti+H1 11

c lffii l t~ 4 ~ ~middot ~ff l ~ ~h i ltlri

1 yen~ middot I ~ I I T ~ gt l+t H+h l+ i j l tfl-l Imiddotmiddot ft+ ++ l f+ Imiddotmiddot I+ I+ middott bulli I 1middot1 I ftt-1shy middot I middot r 11 I IH Ij ~ ~ middotishy J F 1= 6= ~

=f l~iit rtti l lit~ I FS lf~ l=i-+

l-11ffi tt lr 1 ~1 -t =l=Rttl 1ft i- 1 ~ I+ I

~~ lflJ

t I lfl m ~~WFB Lt

41plusmn811 IF I Hir tt ft itttplusmn i I~

1-+++middot

I ~ I (~ ffitrHf1 Ittmiddot ~ l r i H-t-r r HHt m 11 H++ I

bull I I

1_ _ F bullmiddot Imiddotmiddot t-- 1-T h iT

f-t+ ftt I+ I lt + T Imiddot 1

1t _plusmn middot~~ ~- 11shy

=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41

I -1---1-1-+--+--Ti-+-------+----r--shy --r--- -shy + t----+shy ----4-~---+-f----f--+-f--l--1 I t--shy --t-- ---+-shy

J-+-~f--~~ -___l_ ~---

i 1 L~L~-~tr-l----H~4-----~-f------+------+-----+----+---+middot-t-middot-H5000

~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4

I I LID= 2 r--shyr-shyI-shy

I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re

DATA FOR CYLINDERS- LID= 1624 32

FIGURE 12

42

1- bull F - t~ SR rtf f$ -~

bull _ middotshy plusmn- 11 ~

t plusmn jit 1 ~1 ftl middotshy l ~r I Ibull ~- -J

t-+ t ttt l+i ti ~ Ill 1111

--1)-0-- L 0 bull 2 -- o-oshy L0bull4

I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I

l ~jj h4 tt ~t== tIR 1_ -

It- nshy ~ tt~

Iit 1 -h~

I T

pound -- r-+-shy Fshy 7 ~ ~tmiddot

I T1 r - middotshy ~ 1= - -

--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re

DATA FOR CYLINDERS- LD= 2 AND 4

FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i

-~ ~ middotmiddotbull1 bull --

I bullbull LID bull 6

~ -middot - --o--o-- L D bull 8 ~

_ _- --o-0-middot LDc 12

-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-

1 1ltbull -gt r- -~ bullIgt bull ~ - c ~- middot- tgt 4

11 l-~I) bullbull c~~ ~ bullI ~ - li p~

1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T

middot~ ~ m- ~ - ~t plusmn~ 3t i t~ -f--- bullbull - ~~ h middot-

01 0~ 10

Re

-

DATA FOR CYLINDERS - LD = 6 8 AND 12

FIGURE I 4

44

Figures 12 13 and 14 The data for LD values of 16 24

and 32 were nearly the same and have been plotted to gether

i n Figure 12 In addition the curves for the other LD

ratios determined fro m Fib~res 13 and 14 have been drawn

in Figure 12 so that the effect of the length-to-diameter

is clearly shown Figure 13 shows the data for LD values

of 2 and 4 and the curves determined from this data

Firure 14 shows the data for LD values of 6 8 and 12

and the curves determined from this data

The data for flat plates in parallel flow are plotted

in Fi gure 15 A correction factor for the edge effect has

beon used so that the width-to-length ratio is not a

parameter in this plot A portion of the data of Janour

(5 p 31) is also shown in the diagram

The data for fla t plates in perpendicular flow is

plotted in Figures 16 a nd 17 Figure 16 shows the data for

WL values of 2 Also the curves for the three WL ratios

1 2 and 4 have been drawn in the fi gure Figure 17 shows

the data for WL values of 1 and 4 The curves determined

from the data have also been dravm in the figure

45

10~ ~ ~--- -shy

t==Ff1TR=+ iJ+--_-_--r_-_---+-+---+--+-+--_---_-~r-=r~=~+--=---=---=---=--~=--=_~1=_--=_~_-middot~~--+-+-t~ 1 Ll~+--+-- ---jtshyl~t L--+ I

I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy

~ ~B 1) I --o-o- JONES - () - - ~~ p f---j- -~-- e e JANOU R

c gt ~c ~ ------ JANSSEN I 0 0 ~ I

IO ~2=i~~~~~~a=~~f=j= ---- TOM OTIKA bulll= I

~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-

~--~~~~~+--+~+--4-r-~1+-~-middot+1~ ~ --H--~-~~os I i i i-4 ---~T I I f-- t --- li-------~--+-_--+--t-----~~-~_+---_-_-_--+------+-+-__+-[- +_- ___ _______ __+---+-r-+--H----_+--r--------+shy

02 1---+ ----+--------1--+---t-----t--+--++t-+---+-+--+----r----t-----t-t--++i-t------t--------t-----tshy

--

01L----1---l___-J-J-IJ_I-LJJ--L-Jl-l-LLI-I--L-~--L-------_~

10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re

DATA FOR FLAT PLATES- PARALLEL FLOW

FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I

+ r-~middotmiddotmiddot - bull +1 + -t-tmiddot middot~ - bull

bull bull 0 bull bull

-- WL =2 WL 4

---shy W Lbull I

h lt6 bull I -~ bull - ~- bull oshy _ middotbullbull bull bull bull bull +I bull I j-shy bull bull bullbull bull bullbullbullbull J

I ~ ~ ~- -middot ~ ln

C bull middotrmiddot

r - _ ~ --~ - ~ middotmiddot -middot ~ y ~ - middot

I middot

1shy IX ~ 11 - 1_ IC 0 ~_j middot ~rf middot middot middot --

II DSmiddot~~ - l - -shy -

bull bull - - +-shy bull bull bull bull bull bull bull bull bull +

middot-

~ ~ an - ~ middotn - middotn

- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T

+1t LL J-t+fiFt=I I H~ -middotshyH- f-Jshy

plusmni-1t~--ttt+ ~-

e e W L = I - -ltgt-o-- WL = 4

f r f+ r=r_ I

bulltt i=f- 3~ +middot

I l

+ ~ middoti T bull

it I+ ~ bull t ~1 ri j t++t+t++tft bullm H--~+H-t+t-++H-f+t+~HtttH t bull~H-IrttI-H

iH-H u nH m

I

t H+t-~ 1-r f-tj

i it iT -t middotHt I I I I Ill

~middot __

r middotshy

i I r-

f H- jLj f r H rr t~

II

t f f-l -t+tt ~ ==_ =~middot irE

I I

I

I

f

I --

i

t

1 r bull - r

~- ltt++l=tUtt~S-t+t+++~-++U +HJJm~-fl~HHtt1 tttn ll+t-Tt-~- ~ r fH T --r -1 t ---t- -tshy w _+ _ I-shy middotI

-shy -r- + Hbull Hshy t-I --r++ -t iHr -1 H-e-- -t I 1IT 1

1 H-rf-I IJftJ Jf+i+ ~ L

=+shy - tjshy rtmiddotshy ~ -

+ H 1-Jt I tt o =tt ~-

~1 l +fill l plusmn~ fplusmn -shy + I t-

DATA FOR FLAT PLATES PERPENDICULAR FLOW- WL= I 4

FIGURE 17

48

DI SCUSS ION OF RESULTS

Correction and Accuracy of Measurements

After a few pre liminary force measurements with the

spheres and a check with Stokes law (Equation 2) it was

apparent that the drag force on the wire was appreciable

and needed to be considered It was decided to take a

series of measurements with the spheres and calculate the

difference between the measured force and the force calcushy

lated from Stokes law The difference in force could then

be attributed to the drag on the wire If Stokes law is

followed the force on the wire should be proportional to

the velocity

A series of twenty measurements of the force on the

spheres was taken for each oil and the difference between

the measured force and that calcula ted by Stokes 1 law was

determined For each oil this difference as plo tted vs

the velocity The points grouped fairly ell around a

strai ght line nearly passing through the origin The

method of least squares was used to determine the equation

of the line best fitting the da t a The equa tion of the

line for the li bht oil tas found to be

Fe bullbull05605v - oooa (35)

which was determined at about 62 7degF Since the intercept

49

of the line is very close to zero it is believed that the

line is a good indication of the drag on the wire The

equation of the line for the heavy oil was found to be

F - 19llv I oo2o1 (36 ) c shy

which was determined at about 64 2deg The intercept of this

line is also quite close to zero These lines plotted in

Fi poundures 9 and 10 were used throughout the investigation

for the correction factor of the drag on the wires For

the cylinders and flat plates in parallel flow which were

pulled by two wires the values determined from Equations

35) and (36) were doubled For the plates in perpendicular

flow pulled by four wires the correction force was multishy

plied by four

The spring scale had 12 ounce divisions but could be

read to the nearest sixth of an ounce Some of the measureshy

ments of force were under an ounce hence a considerable

spread of the measurements was noticed in the pre liminary

data and throughout the experiment However sufficient

points were obtained so that it was possible to draw a

reliable curve through the data in all casas An analysis

was made to determine the average deviation from Stokes

equation for the spheres It raa found that the average

deviation was 15 1 for the light oil 16 6 for the heavy

oil and 15 9 overall The maximum deviation was 89

50

Inspection of the other data shows that these deviations

are also representative of the cylinders and flat plates

The force measurement is the least accurate part of the

experiment Other insignificant errors are introduced by

a small variation in the temperature This variation was

held to about 10 from the temperature of the calibrated

correction curve The velocity measurements and the

dimensions of the cylinders spheres and pl~ tes are conshy

sidered go od enough so tha t no appreciable errors occur

In order to e l iminate the WL parameter for flat plates

in parallel f l ow an additional factor for the effect of

the edges was subtracted from the measured force Janour

(5 p 27) presented the foll owing equation for the edge

correction for one edge of a flat plate in parallel flow

F ~ lv~ bull (37 ) edge gc

In present work this equation as doubled because both

edges of the plates were submerged in fluid It is assumed

in appl ying this correction that the lowe r limit of a

Reynolds number of 10 proposed by Janour can be extended

close to 0 1

Analysis of Results

Forty of the points for the spheres were used to get

51

the correction factor for the wires The remaining thirty

points are well erouped about Stokes law

The data for cylinders for LD ratios of 16 24 and

32 did not seem to be se gregated therefore these data

were plotted together It would seem that in the low range

of Reyno l ds numbers an LD of 16 and greater can be con shy

sidered an ~nfini tely long cylinder The other LD ratios

of 2 4 6 a 12 provided fairly distinct and separate

lines The best straight lines were drawn through the data

for each of the LD ratios It was evident that in eaeh

case a slope of -1 on a lo g-log graph gave the best straight

line which would indicate that the force varies directly

as the velocity It was possible to develop an empirical

expression relating dra g coefficient Reynolds number and

LD The following equation was obtained from the straight

line plots of Re vs fd for the various LD ratios

(38 )

Equation (38) applies for Reyno l ds numbers from 01 to 10

and for LD ratios of 2 to 16 For LD ratios greater

than 16

10 re (39 )

The data for flat plates in parallel flow is plotted

in Figure 15 after the correction factor for tho edge

52

effect was subtracted When the edge correction is made

no effect of WL ratio is indicated This result would be

expected The data followed a straight line with a slope

of -1 up to a Reynolds number of 2 After that a curve was

dravm connecting the line to that obtained by Janour The

equation for the straight section of the curve is

f - 6 (40)- Re

which applies for Reynolds numbers of 0 1 to 2 0 Here

a gain the force is proportional to the velocity Vfuen

determining drag force for flat plates in parallel flow

the force is first calculated from Equations (40) and (15 )

then the edge correction is added

The effect of the geometric ratios is clearly shown in

the data for flat plates in perpendicul ar flow which are

plotted in Figures 16 and 17 As with the other data the

best straight line was drawn through the various points

for eaoh of the WL ratios Again the line had a slope of

-1 The equation relating fd Re and wL was found t o be

rd 37 (w) -o 3o (41)Irel

which applies for Reynolds numbers of about 05 to 2 0 and

WL ratios of 1 to 4 It is possible but it has not been

proved that Equation (41) is suitable for higher WL ratios

The exponent on WL in Equation 41) is very close to that

53

on L D i n Equation ( 38 )~ It i s possible t ha t these

exponents are t he same but this cannot be sho~~ depound1nitely

until more accura te da ta are available It would be exshy

pected that a s the Reynolds number approaches zero t he

effect of geometric ratios would be the same for cylinders

and fla t pla tes in perpendicula r flow

It is seen in the t a bles of data that occasionally a

ne gative force was obtained because the correction applie d

due to t he wire dra g was greater than the mea sured force

These points obviously are incorrect This occurred only

for the smallest plates in the heavy oil at t he highest

velocities However these knom bad points occur in less

tha n 5~ of the data

It is clearl y shown that for cylinders and plates the

fd increases as L D or W L decreases This is in direct

contrast to Wiesel aberger s investigation However his

work is for hi gher Reynolds numbers at which a turbulent

wake forms bull

Comparison of Results with Other Data and Theoretical So l utions

The data for sphere~ a grees of course with Stokes

l aw since that law was used to determine the correction

factor for the wire Liebster (9 Pbull 548 ) has

54

substantiated Stokes equation

There are no experimental data with which to compare

the results of the cylinders Wieselsbergers minimum

Reynolds number of 4 is above the ran ge covered in the preshy

sent investigation The da ta for the highest LD ratios

(16 24 and 32) does agree almost exactly wi t h the solution

of Allen and Southwell (1 P bull 141) (LD =00) in the range

of Reynolds numbers from 0 1 to 1 0 Allen and Southwells

solution a greed with the data of Wieselsberger (16 p 22)

However the present data is above the theoretical solutions

of Lamb (8 p 112-121) throughout the range of Reynolds

numbers from 0 01 to 1 0 and above the solutions of

Bairstow Cave and Lang (2 p 404) I mai (4 p 157) and

Tomotika and Aoi (15 p 302) for Reynolds numbers of 0 1

to 1 0 Allen and Southwells solution a grees dth both

Wieselsberger 1 s a nd the present data Their solution and

the present data represent the best means for predicting

drag coefficients for flow over long cylinders for Reynolds

numbers of 0 01 to 10 It should be remembered that the

o t her solutions should a gree with eac h other since they

were all essentially derived by linearizing the Na viershy

Stokes equation

The data for flat plates in parallel flow is

55

considerably above the theoretical solutions of Janssen

(6 p 183 ) and Tomotika and Aoi (15 Pbull 302) However

Fi f~re 15 shows that a smooth transition occurs bet een

the present work and the data of Janour (5 P bull 31) The

present data considerably extend the experimental inforshy

mation previously available for laminar flow paral lel to

flat plates In the re gion of Reynol ds numbers less than

2 the drag coefficient is shown to be inversely proportional

to the Reynolds number Janours data covers a range of

Reynolds numbers from 11 to 1000 The results of the

present investigation line up with Janours results which

in turn on extrapolation to higher Reyno l ds numbers

(greater than 1000) make a smooth transition into Blasius

curve represented by Equation (10) At Reyno l ds numbers

greater than 20 000 the drag coefficient is inversely proshy

portional to the square root of the Reynolds number

The data for flat plates in perpendicular flow is conshy

siderably above the solutions of Tomotika and Aoi

(15 p 302) and Imai (4 p 157 However their solutions

f or cylinders and plates in parallel flow are also below

the present data Also it should be remembered that their

solutions are for infinitely wide plates If a value of

WL of above 100 is used in Equation (41) then the present

data and the solutions of Tomotika and Aoi are fairly close

56

The present results indicate that Equation (41~ can be

used with an accuracy of 15 to 20 within the limitations

of the equation (WL 1 to 4 Re = 0 05 to 2)

57

SUM RY AND CONCLUSIONS

Only a small amount of work has been done in the past

on the study of laminar flow over immersed bodies There

are many areas in the chemical process industries and the

field of aeronautics where this information would be very

helpful The purpose of the present investi gation wa s to

study the almost totally unexplored range of Reynol ds

numbers from 0 01 to 10

Drag coefficients have been determined for spheres

cylinders and flat plates in paralle l and perpendicular

flow The drag coefficients have been plotted as a

function of the Reynolds number with dimension ratios as

a parameter on lo g-log graphs The best straight lines

have been drawn through the data In all cases these lines

had a slope of -1 hich shows that the dra g coefficient is

inversely proportional to the Reynolds number at very low

Reynolds numbers for all shapes and dimension ratios The

following equations have been determined from the data

For cylinders

fd - 27 L -0 36 (38 ) - Re ())

which applies for Reynolds numbers of 0 01 to 1 and LD of

2 to 16 For LD greater than 16 the equation is

58

(39)

For flat plates in parallel flow a correction factor has

been applied to account for the edge effect The equation

which applies for Reyno l ds numbers of 0 1 to 2 is

f 6Re

(40)

For flat plates in perpendicular flow

f d

- 37 - Re (w) t -

0 bull 30 (41)

wbieh applies for W L of 1 to 4 and Reynolds numbers of

0 05 to 2

It is concluded tha t Equations (38-41) give the best

values of drag coefficients within an accuracy of 20~ for

the range of Reynolds numbers that were considered Also

it is evident that the dimension ratios are a n important

factor in determining the drag coefficient for a given

Reynolds number Furthermore the drag coefficient inshy

creases with decreasing values of L D or W L for a constant

Reynolds number The da ta obtained in this investi gation

compare favorably with the other experimental data and with

some of the theoretical sol utions It should be remembered

that when comparing the experimental data with theoretical

solutions that practically all of the solutions are for an

infinitely long cylinder or an infinitely wide plate

It is recommended tha t the present apparatus be

59

modified so that a force of 001 pound can be measured

Also it would improve tho accuracy to set up a constant

temperature bath so that the temperature of the oil can not

vary over 02degF A few check points on the present data

is all that is necessary to confirm the validity of

Equations (38- 41) It is also r ecommended that only SAE 140

oil be used and that 2 inches should be the minimum plate

width and cylinder length to be studi3d These conditions

would help to maintain the accuracy of the correction force

for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft

M mas s lb m Re Reynolds number Dvf= -ltr w width ft

a area sq ft

b characteristic length ft

d diameter ft

f drag coefficientfd

gravitation constant l b mft gc 2= 32 17 l b _ rsec

1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions

X xbullcoordinate ft

y y- coordinate ft

o( vorticity

time sec

viscosity lb m ft -sec

kinematic viscosity ft 2sec

circumference diameter = 3 1416

3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY

1 Allan D N de G and R v Southwell Re laxation methods applied to determine the motion in two di shymensions of a viscous fluid past a fixed cylinder Quarterly Journal of Mechanics and Applied Mathe shymatics 8 129-145 1955

2 Bairstow L B M Cave and E D Lang The reshysistance of a cylinder moving in a viscous fluid Philosophical Transactions of the Royal Society of London ser A 223383- 432 1923

3 Goldstein Sidney The steady flow of viscous fluid past a fixed spherical obstacle at small Reyno l ds numbers Proceedings of the Royal Society of London ser A 123225-235 1929

4 Imai I A new method of solving Oseens equations and its application to the flow past an inclined elliptic cylinder Proceedings of the Royal Society of London ser A 224 141-160 1954

5 Janour Zbynek Resistance of a plate in paralle l flow at low Reyno lds numbers Washington Nov 1951 40 p National Advisory Committee for Aeronautics Te chnica l Memorandum 1316)

6 Janssen E An analog solution of the Navier-Stokes equation for the case of flow past a f l at plate at low Reynolds numbers In 1956 Heat Transfer and Fluid Mechanics Institute (Preprints of Papers) p 173-183

7 Knudsen James G and Donal d L Katz Fluid Dynamics a nd Heat Transfer Ann Arbor University of Michigan 1953 243 p (Michi gan University Engineering Research Bulletin no 37)

8 La~b Horace On the uniform motion of a spherethrough a viscous fluid Philosophical Magazine and Journal of Science s~r 6 21112-121 1911

9 Liebster H Uben den widerstrand von kugeln Annalen Der Physik ser 4 82 541- 562 1 927

63

10 McAdams William H Heat transmission 3d ed New York McGraw- Hill 1954 532 p

11 Pai Shih- I Viscous f l ow theory I Laminar flow Princeton D Van Nostrand 1956 384 p

12 Prandtlbull Ludwi g Es sentials of fluid dynamics London Blackie amp Son 1954 452 p

13 Relf i F Discussion of the results of measure shyments of the resistance of wires with some additionshyal tests of the resistance of wires of small diame shyters In Technical report of the Advisory Committee for Aeronautics London) March 1914 p 47 - 51 (Report and memoranda no 102 )

14 Stokes George Gabriel Mathematical and physical papers Vol 3 Cambridge University Press 1922 413 p

15 Tomotika s and T Aoi The steady flow of a viscous fluid past an elliptic cylinder and a flat plate at smal l Reynolds numbers Quarterly Journal of Me chanics and Applie d Ma thematics 6 290- 312 1953

16 Wieselsbergo r c Versuche Ube r der luftwiderstand gerundeter und kant iger korper Er gebnisse der Aeroshydynamischen Versucbsansta l t Vol 2 G~ttingen 1923 80 p

APPENDIX

64 EXPERI~ffiNTAL DATA

TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)

Veloci ti Force Measured Corrected

Temp Re fd

SEhere No 1 Lisht oil

2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8

Sphere No 1 - Heavy oil

05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270

Sphere No 2 - Light oil

09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)

Sphere No 3 - Li ght oil

09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18

Sphere No 4 - Litht oil

09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00

Sphere No 4 - HeavY oil

05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )

Ve lo citt Force Measured Corrected

Temp He fd

Cylinder No 1 LD =8 - Light oi l

09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51

Cylinder No 1 - Hea~ oil

05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48

Cylinder No 2 - L D = 4 Li ght oil

09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)

Cylinder No 2 - Heavy oil

05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93

Cylinder No 3 - LD = 2 - Light oil

09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92

Cylinder No 3 - Heayy oi l

05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160

Cylinder No 4 - LD 2 - Light oi l

09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25

Cy1inder No 4 - Hea~ oil

05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95

Cylinder No ~ 5 - L D = 16 - Li ght oil

09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)

Cylinder No 6 - LD 8 - Light oil

09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63

Cylinder No 6 - Rea oil

05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8

Cylinder No 7 - Lp 4 - tieht oil

09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35

Cylinder No 8 - Lp =2 - Li ght oil

09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04

C~linder No 8 - Hea Vf oil

05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15

Cylinder No 9 - L D = 24 - Light oil

09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1

Cylinder No 10 - LD 12 - Lirht oil

09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37

Cy11nder No 10 - Heavy oil

05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07

Cylinder No 11 - L - 6 Li ght oil

09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16

Cylinder No 1 1 - He a Yil oil

05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40

Cylinder No 12 - LD 4 Li ght oi l

0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091

Cylinder No 13 LD - 32 - Light oil

09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69

Cylinder No 1 3 - Heavy oil

05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387

Cylinder No 14 L - 16 Li ght oil

09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8

Cylinder No bull 15 LD 8 Lieht o i l

09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01

Cylinder No 1 5 - HeayY oil

05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86

Cylinder No 16 - L D 6 Light oil

09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10

C~11nder No 16 - Hea~ o~_

05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV

Data For Flat Plates - Parallel Flow

(2) (3) (4) 5) 6)

Force Temp Re f 1easured Corrected -

Pla te No l a - W L =4 - Light oil

02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19

Plate No la - Heavy oil

03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102

Plate No lb WL - 1(4 - Lisht oi l

02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27

Plate No lb - HeaYI oi l

05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060

Plate No 2a - WLL 2 Li ght Oi l

09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98

Plate No 2a - HeaI oil

05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64

Plate No 2b - WL 12 - Light oi l

09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46

Plate no 2b - Heavy oil

05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65

Plate No 3 W L = 1 - Light oil

09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05

Plate No 3 - Heavy oil

05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35

Plate No 4a - W_L 1_2 - LiEht oil

09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92

Plate No 4a - HeaYI oil

05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38

Plate No 4b - w_L = 2 Light oil

09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10

Plate No 4b - Heavy oil

05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l

Iata For Flat Plates - Perpoundendicular Flow

(1) (2) (3) (4) (5) (6)

Veloci tz Force Temp Re fd Measured Corrected

Plate No 1 - WL = 4 - Light oil

09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89

Plate Nv 2 - WL bull 4 Light oil

0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39

Plate No 2 Heavy oil

05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840

Plate No 3 - WL =4 - Light oil

09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99

Plate No 5 - WL - 2 - Li ght oil

09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27

Plate No 5 - He a~ oil

05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810

Plate No 7 - W L 2 - Light oil

09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42

Plato No 7 - Hea~ oil

05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64

Plate middotNo 8 - wi_L =2 - Lifiht oil

09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397

Plate No 8 - HaaI oil

05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84

Plata No 9 W L bull l - Light oil

09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)

Plate No 9 - Ieavy oil

bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7

Plate No 10 - wLL bull 1 - LiBht oil

09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61

Plato No 10 - Heavy oil

05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25

Plate No 11 - wLL 1 - L1f3ht oil

09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28

Plate No 12 - W L bull 1 - Light oil

09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89

DENSITY AND VISCOSITY C LIBRATION

TABLE VI

rependence of Denaitx on Temperature

Temp bull degF Density-lbmcuft

Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90

I J 1_ middotmiddot - __L-9---r--+----- middot-middot--- --_1---1--+ _middot middot middot r middot~_middot+middot~-+-+-4---+-l

~~ ~ middot middotmiddot 1 middot

I _cmiddot --+middotmiddotmiddot i middot middot middot bull bull middoth-middot j t--+~- middot middot 1 ~t ~ ~-- middotD IJmiddotmiddot---- middot middot middot D iJ middot middot middot -~ Imiddot -shy middot bull middot -shy

DEPENDENCE OF VISCOSITY ON

TEMPERATURE- LlGHT OIL

FIGURE 18

i t ~ ir bullbull middot

H

- ~ -ii li

v I -+- -- -~-- -0~- ~-+-+-~middot+middot --+J-_-f+-c-1]shyH-+-c+--f=t-4-+-+~~---+--1- -+-+- --- ~ -+-+-i~---1middot-

-L --- l-+-+++1-1 -~ --t~--1- --~- ~+-middot j----- -~ -i- -1-~ -middot-middot~--+--f-+-+- ~-- h 1-+-+-t-+-+--1-+-t-+- +- L ~~ --~ -------t- -1-f~ r ishy

J -1Imiddot+-I T - --- r- -~- -lmiddot--- -~-~- T pod---lgt-1--+-t-+-+-+-t------rmiddot-i

middot+-- ~ e +-- --+- ~- ~~ 3 t- - ~- - 65 +- -f- - 1 e1-l --- -middot -+-+~bulla+__~Jmiddot --shy1 I I +-+rH-r~1 ~ - i~-t-f- middot l I cLt

DEPENDENCE OF VISCOSITY ON TEMPERATURE HEAVY OIL

FIGURE 19

92

SAMPLE CA LCULATI ONS

1 Calculation of Drag Force on the Wire

Example l-inch sphere (62 4deg) 129 rev sec 34 in pulley Li ght oil

Velocity - 0 196 ft x 1 29 rev 0 254 ft sec rev sec

Density - 56 1 lbm cu ft

Viscosity bull 2 06 lbm

ft -seo (Figure 18 )

Diameter - 0 0833 ft

Reynolds number shy

~a 0 0833 ft (254 ft sec )( 56 1 lbm) 0 576 A 2 06 l b m

ft3 ft-sec

Tota l measured force including weight - 0 156 lb

Wt of ball - (485- 56 lbm)(l ft )3 0 130 lb 6 3 12

ft

Measured drag force on sphere - 0 156 - 0 130 0 026 lb

fd (Stokes) - o ~~S 41 6

Force (Stokes ) shy2

41 6 (561 lb mft 3 )(0 254 ft sec t(0 00545 ft ) 2(32 2 lb m ft lb f sec2

o ol29 lbf

93

Drag force on wire - 0 026 lb - 0 0129 lb 0 0131 lb

for F ow)

4 11Example l cylinder 12 dis 0 4751 revsec 34 pulley Light oil

Ve locity - (Same method as part 1) 0 09329 ft sec

Density bull 56 1 lb mcu ft

Viscosity - 2 05 l b m ft -sec (Figure 18 )


Reyno l ds number - (Same method as part 1) 0 105

Measured drag force - 0 02083 lb

Correction force f or wire (Figure 9 ) 0 00886 lb

Drag force on cylinder - 0 02083 1b -0 00886 lb 0 01197 lb

fd - o 01197 l b r ( 32 2 lbmft lb rsec~(2)

( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5

3 Calcul ation of Dra Coefficient for Flat Plate - arallel Flow

Example 1 in 1 4 in w (62 4deg ) 0 4751 rev sec 3 4 u pulley Li ght oil

94

Ve locity - (Same as part 2) 0 09329 ft s ee

Density - 56 1 lb cu ft m

Viscosity - 2 06 l b mft - sec (Fi gure 18 )

Length - 0 0833 ft

Reynolds nutlber - (Same method as par t l ) 0 212


Correction force for wire - 0 00886 lb (Fi gure 9 )

Correction force for edge effect shy

3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb

2(32 2 lb ft lb sec ) ft -sec m f

Drag force on plate shy

0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b

fd - 001038 (2 (32 2 lbmft lbfsec 2 ) --2(56 1 lb cu ft )( 0 09329 ft sec ) ( 0 055~6 ft 2 )m

24 6

APFROVED T


In 0hrrg of laJar




Drtc tbrclr la prrrontr a h4ul^r-J-trlqql

lfypcd by ftrcdeetr Or Joncr

i

ACKNOWLEDGEMLNT








bull bull bull


bull bull

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ii

TABLE OF CONTENTS

Pa ge




















Foree Measurements


25

26

26

30

35

35

36





ii i


Page









Nomenclature 60







iv


Fi gure Page




















v


Figure Page





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bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

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11 ~ ~ - I bull J


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f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

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1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




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0 1

0 1 10

f I t

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2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

i

ACKNOWLEDGEMLNT








bull bull bull


bull bull

bull bull

bull bull bull bull

bull bull

bull bull bull bull

bull bull

bull bull

bull bull


ii

TABLE OF CONTENTS

Pa ge




















Foree Measurements


25

26

26

30

35

35

36





ii i


Page









Nomenclature 60







iv


Fi gure Page




















v


Figure Page





bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6




bull bull bull


bull bull

bull bull

bull bull bull bull

bull bull

bull bull bull bull

bull bull

bull bull

bull bull


ii

TABLE OF CONTENTS

Pa ge




















Foree Measurements


25

26

26

30

35

35

36





ii i


Page









Nomenclature 60







iv


Fi gure Page




















v


Figure Page





bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6





ii i


Page









Nomenclature 60







iv


Fi gure Page




















v


Figure Page





bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6



iv


Fi gure Page




















v


Figure Page





bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6




v


Figure Page





bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6


bull bull bull bull

bull bull bull

bull bull bull

bull bull bull


vi

LIST OF TA BLES

Table Pa ge











LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6



LJTRODUCTI ON





















2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

2


followin g equation

1)

















solutions

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

3
















F 6ffA vr (2)




fd - 24-re (3)



4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

4



f - 24 1d - Re (1 r 3Re) (4) I6












f - 8 ff (5) d - Re (2002 - ln Re)








5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

5

I 00

50

2

10

I I

i I

middoti



It

I

I

--

i

-


11 ~ ~ - I bull J


I middot ~

t--i ~--~+-+-~4-4-~-~H---~~~~~~~~~

f L bull l

01 2 5 10 2 5 Re


Fl GURE I

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

1

6

a-

rr

- ~middot

e


LAN I

--middot

J middot bull bull

-=

bull JIo



1 oL-bull~~~~~~~~~~~~~~~o~--~~~~~~~~~~~~~o2 e 1


FIGURE 2

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

7





















4 0




5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

5

2

0 1

0 1 10

f I t

501----+--+-+--+-JUL

~

bullt

bullJ bull bull I


o o INAI - JANSSEN


~ bull t bull

~ ~ - middot

-= - middot ~

2 5 10 2

Re

1


FIGURE 3

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

9

100

~0

20

10

-

2

I

01 2 10 10

Rt

I I I I I -I I

I

--- --+--r f-- ----Il -- - - ----

-middot


I I - -- --- - r-- - --r

-

H~ middotmiddot-

I I--I l 1I I )

--

I i

I i II I I

I

I ---~-- I

I

I

I

- - -- ----r-- - l - r---1--t---middot~

1 -~-~ - imiddot-- --l=l-----

- - -- --r-1---J I I

J I --r-f--1-

I H-I 1--

I I

I II

I I I ~-

I I

I I

II

+ --f- --

~ t-

-- f--

--

f---

~

0 0 I MAl

-

-- TOMOTIKA a AOI

I

1-

I I

I r-

f I --r-

I I I I

r-f- I I

I

i 2

- r-

middot-t-

-f--middott--

- t-

- 1-t--

- -~

f---- cmiddot-

f-1---f-- -

f--___ ~-I

I I

-- -1-


PERPENDICULAR FLOW

FIGURE 4

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

10



















u = d~ v = Jtf (7) d y d X





11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

11


J dX dJ Jj dX (8)

--lt ( 9 )








Experimental Data











fd 1328 12 (10)(Re )

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

12



2 90fd (He) 601 11)




















13

























14











Aoi




coincide









15




numbers















numbers



flow

16









of the medium









m f av (12)





to

17

mv p av 2

(13 )






















12 f av2 bull

18






v velocity and




14 )









19

F 12 f f aw v 2

(15)go


aw wetted area


follows 2

F 12 fd f b v (16) go














20






obtained

L b (17)

g - L - b - -- (18)v v M f L3 3 (19)=f b F e F (20 )




Thus

-- f b2 v2 (21)gc 2F e F

and

A __ fbv 22 ) Le


groups

F g1T 1 = c -- (23)

and

21

1T 2 P bv A

Re bull 24)




another so that















- g (26 ) =c f

and

22

27)



respectvely

t bull time






J u f J v 0 (28 )Jx n















du d t

j U

du d X

I v d u c) Y

-~ ( ~ J x

(29)

and

(30)














24


(32)2 = g ~ AAV u c(JX

and

2 = g ~ (33) V v c J y bull


















25
















26























27

MOTOR

SPEED REDUCER

WEIGHT

-SPRING SCALE

SPACER -F====t

-FINE WIRE

I ICOOLING WATER I

EXIT IL ___ JI

1PLA1E 1

L_-- J

I

I OIL DRUM

I

I

I I


INLET


FIGURE 5

28

APPARATUS LEFT VIEW

FIGURE 6

29


FIGURE 7

30






the top












not shown






31

TA BLE I


sehe re s

No D-in Material


Cylinders





32




-------

1 I

l 11 i~

~

bull J~

-- __4t

-----

---middot-1~

II ~

------- ~


34




35






















36




be less tha~ 0 5~

force Measurements






the same

37
























CD_ bull 0 G 0

03

Tshy02

01

10 20 30 410 50 60 70 80

VELOCITY- FTJSEC


FIGURE 9










FIGURE 10

40





iU=ff=t 1 +~ t_ - ~ r 111= t h=

I middot

t= IE I 1 1


(~ l h+middot

ru HmiddotHti+H1 11





~~ lflJ

t I lfl m ~~WFB Lt


1-+++middot


bull I I




=a~ 1~ - =itf lttti

H I

=

DATA FOR SPHERES

FIGURE II

41


J-+-~f--~~ -___l_ ~---


~--~--~-------+------+-+--+--+- +-~-~---------------- -1 r- ~ -~- i - ---+------- f--- f-shy

2 0 0 0 1---i------+----+---+-----1---t--+-+ I I I

LID =1624 32 LID =12

t---~1 - --shy j _j - -shy+--+-if-++ I

~ _0 - 1000

~00 p

0-

--+-l-+-1--+--------+--+---+---4-1-shy

L D= 8 L D = 6

---shy LID=4


I

10~--~~~~~~~~~~~~~~--~~~~

01 02 05 10 20 50 10

Re


FIGURE 12

42






I I

1ill ie~ ~

t-

I I

middotr-I II

I I

I


It- nshy ~ tt~

Iit 1 -h~

I T



--+++ +t ~ It ti H

11111

Llmiddotmiddot T

lt jTlttn

02 05 ro 20 50 10 Re


FIGURE 13

L_

plusmn -

- lq

1ffi 11

20

43

~000

2000

1000

~00

200

100

50

20

1020 50 10 20

I I

I

I I I

if- -- i





-middot 0

~ p --

-( ~~~ middot li

~

~cp ~~ Qiy_

~~0 (~ -~~ ( rl~~~ ~~ 13 y I

~ f-~ ~c

)j middot-



1~~ bullI

- ~ -~ ~ lt

_ tLbull 1-

-- ~ - I r-- t

- - -~ T


01 0~ 10

Re

-


FIGURE I 4

44





















45

10~ ~ ~--- -shy


I

P------ _l -- --1---L i

20 ~-- I ~g I --- - ---+-- r t L_shy


c gt ~c ~ ------ JANSSEN I 0 0 ~ I


~~n ~~--~~~~~~o~~~~~--4- NDCIgttl o shy

-



--


10 20 50 100

I Ir--------+-f------+--+1----+-+-+---J-++-------r-1-+------1-t-+----t---+-----+1--+--1

[-rl- I_--t--+---+-t---i--~r-t-t--1- t-

AOI ---t-+--+---t---t-H

~~~i-+---t-~-+---r+~

~~ I -+-i~-t__li--111~1t---t----~ +t--l

1-t---t--+----r--tNN

--~-~+-~~-~~~4---t----+-++~~~11~+-f-~~

0 1 02 05 2

Re


FIGURE 15

46

-

I ~ V

--- v

IV

1

bull 1 n I

I



-- WL =2 WL 4

---shy W Lbull I





I middot




middot-


- -- -

DATA FOR FLAT

PERPENDICULAR

FIGURE

PLATES

FLOW- WL=2

16

47

1 _ bullbull I

T




f r f+ r=r_ I


I l

+ ~ middoti T bull


iH-H u nH m

I

t H+t-~ 1-r f-tj


~middot __

r middotshy

i I r-


II


I I

I

I

f

I --

i

t

1 r bull - r








FIGURE 17

48












the velocity












49













plied by four












50




















close to 0 1

Analysis of Results


51

















(38 )



than 16

10 re (39 )



52







f - 6 (40)- Re












rd 37 (w) -o 3o (41)Irel





53


















wake forms bull





54






















Stokes equation


55

























56




57



















For cylinders

fd - 27 L -0 36 (38 ) - Re ())



58

(39)




f 6Re

(40)


f d

- 37 - Re (w) t -

0 bull 30 (41)


0 05 to 2















59










for the wire

60

~WMENCIATURE

Symbol Dimensions

A area sq ft

D diameter ft

F force lb f

L length ft


a area sq ft


d diameter ft



1 length ft

m mass l b bullm

p pressure lbrsqft

r radius ft

t time see

u velocity ft sec

v velocity ft sec

w width ft

61

Symbol Dimensions


y y- coordinate ft

o( vorticity

time sec




3density lb m ft

function

stream function

Laplacian operator

infinity

Subscripts

c corrected

f force

1 l iquid

m mass

p projected

s solid

w wetted

62

BI BLIOGRAPHY










63








APPENDIX


TABLE II

Data For SEheres

(1) 2) (3) 4) 5) (6)


Temp Re fd


2250 0230 0112 62 2 384 87 3

2539 0178 0044 62 2 432 25 4

2892 0283 0 129 62 2 493 57 0

4228 0387 0158 62 2 720 33 0

5919 0543 0219 62 2 1008 23 3

7610 0700 0246 62 2 1 296 15 8


05496 01562 00311 64 3 0381 378 5

0916 02604 00653 64 3 0635 286 2

1282 03646 00995 64 3 0890 222 6

1649 04887 01535 64 3 114 207 6

09843 03125 01043 63 6 0633 395 8

1641 05208 01871 63 6 106 255 5

2297 07292 02701 63 6 148 188 3

2953 08854 03010 63 6 190 1270


09639 01050 00570 62 2 219 125 8

1606 01600 00780 62 2 365 63 4

2250 01900 00720 62 2 512 30 0

2892 02600 0106 62 2 658 26 2

2539 02600 0126 62 2 576 41 2

4228 04500 02210 62 2 960 26 0

5919 08900 05660 62 2 1344 33 9

7610 10400 05860 62 2 1730 21 3


05496 02083 00832 64 3 0508 570 0

09160 03125 01174 64 3 0848 289 7

1282 04687 02036 64 3 119 256 3

1649 05208 01856 64 3 153 1413

65

(1) (2) (3) (4) (5) (6)


09~29 01042 00599 62 3 310 65 95

1555 01562 00770 62 3 519 30 51

2177 03125 02005 62 3 727 4054

2799 04167 02678 623 935 32 76

1343 01562 00889 63 1 463 47 22

2238 03125 01951 63 1 772 37 32

3134 04687 03010 63 1 1 082 29 37

4029 04687 02509 63 1 1 390 14 81


05496 03125 01874 64 3 0754 585 5

09160 0~646 01695 64 3 126 190 7

1282 05729 03078 64 3 176 176 8

1649 06250 02898 64 3 226 100 6

03974 01562 00602 65 8 0598 3599

06624 02604 01139 65 8 0997 245 1

09273 03125 01152 65 8 140 126 5

1192 03646 02479 65 8 180 7753

09843 04687 02605 636 125 253 8

1641 07812 04475 63 6 209 156 9

2297 09896 05305 63 6 292 94 90

2953 10940 05096 63 6 375 55 18


09329 01562 01119 62 3 416 68 86

1555 02604 01812 62 3 694 40 13

2177 03125 02005 623 973 2265

2799 03646 02157 623 1 249 14 75

1343 02604 01931 63 3 623 57 34

2238 03125 01951 63 3 1 040 20 86

3134 04167 02490 63 3 1 454 1358

4029 05208 03030 63 3 1 8 70 10 00


05496 02083 00832 64 3 101 145 3

09160 03125 01174 64 3 168 73 83

1282 04687 02136 64 3 235 68 55

1649 05208 01856 64 3 302 36 01

03974 02604 01644 65 8 oao 549 1

09273 03646 01673 65 8 187 102 7

06624 03125 01660 65 8 133 199 6

66

(l) ( 2 ) (3 ) ( 4 ) ( 5 ) ( 6 )

1192 03646 01167 65 8 241 34 06

09843 05729 03647 63 6 167 198 6

1641 08333 04996 63 6 279 97 85

2297 09375 04784 63 6 391 47 85

2953 11460 05616 63 6 502 33 98

67

TABLE III

Data For Cylinders

1) (2) (3) ( 4 ) (5) 6 )


Temp He fd


09329 02083 01197 62 7 0537 454 2

1555 03125 01541 62 7 0895 210 3

2177 04167 01 927 62 7 125 1342

2799 04167 01189 62 7 161 50 10

1343 02604 01258 62 5 0765 230 2

2238 04167 01819 62 5 128 119 9

3134 05208 01854 62 5 179 62 33

4029 06250 01894 62 5 230 38 51


05496 03125 00623 64 8 0129 670 5

09160 05208 01306 64 8 0216 506 0

1282 06250 00948 64 8 0302 187 5

bull1649 08333 01629 64 8 0388 194 8

03974 bull02604 00684 65 8 0101 1409 bull

06624 03125 00195 65 8 0168 144 5

09273 04167 00221 65 8 0235 83 58

1192 05729 00771 65 8 0302 1764

09843 05208 01094 63 6 0211 350 2

1641 08333 01659 63 6 0352 200 3

2297 11460 02278 63 6 0493 1404

2953 14060 02372 63 6 0633 88 48


09329 01562 00676 62 7 108 128 2

1555 03125 01541 62 7 180 105 2

2177 03125 00885 62 7 250 30 82

1343 02083 00737 62 5 153 67 43

2238 04167 01819 62 5 255 59 93

3134 06250 02896 62 5 357 48 68

4029 07292 02936 62 5 460 29 85

68

(1) (2) (3) (4) (5) (6)


05496 04167 01665 64 8 0258 896 0

09160 05729 01827 64 8 0432 354 0

1282 08333 03031 64 8 0604 299 7 1649 09375 02671 64 8 0776 159 7 03974 02083 00163 65 8 0202 1 67 8 06624 04167 01237 65 8 0336 384 2 09273 04687 00741 65 8 0470 140 1 1192 05208 00250 65 8 0604 28 60 09843 05208 01044 63 6 0422 175 1 1641 09375 02701 63 6 0704 163 0 2297 11460 02278 63 6 0986 70 2 2953 14580 02892 63 6 127 53 93


09329 02083 01197 62 7 215 113 5

1555 03646 02062 62 7 360 70 35

2177 04167 01927 62 7 502 33 55

2799 05208 02230 62 7 644 23 49

1343 03646 02300 62 5 306 105 2

2238 06250 03902 62 5 510 64 28

3134 07292 03938 62 5 714 33 09

4029 07292 02936 62 5 920 14 92


05496 03646 01144 64 8 0517 307 8

09160 06250 02348 64 8 0864 227 4

1282 07812 0 2510 64 8 121 124 1

1649 08854 02150 64 8 155 64 27

03974 0 3 125 01205 65 8 0404 620 3

06624 03646 0071 6 65 8 0672 132 6

09273 05729 01783 65 8 0940 168 5

1192 0625 01292 65 8 121 73 87

09843 06771 02607 63 6 0844 218 6

1641 10940 04266 63 6 141 128 7

2297 1 5100 05918 63 6 197 91 14

2953 16150 04462 63 6 253 4160


09329 02604 01738 62 7 322 109 9

1555 04167 02583 62 7 538 58 75

21 77 05729 03487 62 7 755 40 50

69

(1) (2) (3) 4) (5) (6)

2799 05729 02751 62 7 967 19 32

1343 04167 02821 62 5 459 86 03

2238 05729 03381 62 5 765 37 14

3134 07292 03938 62 5 1 071 22 06

4029 08854 04498 62 5 1 380 15 25


05496 04687 02185 64 8 0775 392 0

09160 06771 02869 64 8 130 185 3

1282 08854 03552 64 8 183 116 1

1649 0 9896 03192 64 8 233 63 61

03974 03125 01205 65 8 0606 413 6

06624 05729 02799 65 8 101 345 8

09273 06771 028 25 65 8 141 178 1

1192 08854 038 96 65 8 181 148 6

0 9843 07812 03648 63 6 127 204 0

1641 12500 05826 63 6 211 117 2

2297 17190 08008 63 6 296 82 29

2953 20310 bull 08622 63 6 3 80 55 95


09329 02083 01197 62 3 0525 227 1

1555 03646 02062 62 3 0875 140 7

2177 05208 02960 62 3 123 103 3

2799 6250 03272 62 3 158 68 94

1343 03125 01779 62 5 0765 162 7

2238 04687 02339 62 5 128 143 0

3134 06771 03417 62 5 179 57 43

4029 08854 04498 62 5 230 45 74


05496 03125 00623 66 7 0148 335 2

09160 06250 02348 66 7 0247 454 8

1282 07812 02510 66 7 0346 248 2

1649 09375 02671 66 7 0445 159 7 bull03974 03125 01205 65 8 0101 1240 bull 06624 bull04687 01757 65 8 0168 651 1 09273 06250 02304 65 8 0235 435 6 1192 06771 01813 65 8 0302 207 4 09843 06671 02607 63 6 0211 437 2 1641 11980 05306 63 6 0352 320 3 2297 16150 06968 63 6 0493 214 7 2953 18750 07062 63 6 0633 131 7

70

(1) (2) (3) (4) (5) (6)


09329 02083 011 97 62 3 105 113 5

1555 04167 02583 62 bull 3 175 88 12

2177 05208 02968 62 3 245 51 67

2799 06250 03272 62 3 315 34 47

1343 04167 02821 62 5 153 129 0

2238 06250 03902 62 5 255 64 28

3134 08333 04979 62 5 357 41 83

4029 06250 01894 62 5 460 9 63


05496 03646 01144 66 7 0297 3078

09160 0625 02348 66 7 0494 227 4 1282 06771 01467 66 7 0692 72 64 1649 08333 01629 66 7 0890 48 7 03974 03125 01205 65 8 0202 6203 06624 04167 01237 65 8 0336 192 1 09273 05208 01262 65 8 0470 119 3 1192 06250 01292 65 8 0604 73 87 09843 07292 03128 63 6 0422 262 3 1 641 11460 04786 63 6 0704 144 4 2297 16150 06968 63 6 0986 107 3 2953 18750 07062 63 6 127 65 8


09329 03125 02239 62 8 215 131 7

1555 0468 7 03103 62 8 358 52 93

2177 06250 04010 62 8 502 34 90

2799 07292 04314 62 8 646 22 72

1343 04167 02821 62 5 306 64 50

2238 06771 04423 62 5 510 36 43

3134 09375 06021 62 5 714 25 29

4029 09896 0554 62 5 920 1408


05496 03646 01144 66 7 0594 153 9

09160 06250 02348 66 7 0988 113 7

1282 07812 02510 66 7 138 62 05

1649 09375 02671 66 7 178 39 92

71

(1) (2) (3 (4) (5) ( 6 )

03974 03125 01205 65 8 0404 310 1

06624 05208 02278 65 8 0672 211 0

09273 06771 02825 65 8 0940 1335

1192 07292 02334 65 8 121 66 74

09843 09375 05211 63 6 0844 218 5

1641 14580 07906 63 6 141 119 3

2297 17710 08528 63 6 197 65 89

2953 19270 07582 63 6 253 35 35


09329 03646 02760 62 3 315 8 7 24

1555 06250 04666 62 3 524 53 06

2177 08333 06093 62 3 735 35 35

1343 05208 03862 62 5 459 58 8 7

2238 08333 05985 62 5 765 32 85

3134 10420 07066 62 5 1 071 19 79

4029 11460 07104 62 5 1 380 12 04


05496 04687 02185 66 7 0891 196 0

09160 0 78 12 03910 66 7 148 1 26 3

1282 09896 04594 66 7 208 75 71

1649 11980 05276 66 7 267 52 58

03974 03646 01726 65 8 0606 296 1

06624 05729 02799 65 8 10 1 172 9

09273 07812 03866 65 8 141 1 21 8

1192 09896 04938 65 8 18 1 94 14

09843 10420 06256 63 6 127 174 9

164 1 16670 09996 63 6 211 100 6

2297 218 10 12688 63 6 296 65 15


09329 03125 02239 62 7 0537 283 0

1555 0468 7 03103 62 7 0895 141 1

2177 06250 04010 62 7 125 93 05

2799 07292 04314 62 7 161 60 57

05441 01 042 00592 63 1 0315 220 0

09068 02083 01218 63 1 0528 163 0

1270 03125 01 861 63 1 0738 126 9

1632 03646 01976 63 1 0948 81 60

1343 03646 02300 62 6 077 1 40 21

72

(1 (2) ( 3 ) ( 4) ( 5 ) ( 6 )

2238 06250 03902 62 6 1 28 85 68

3134 08854 05500 62 6 179 61 60

4029 09896 05540 62 6 230 37 54


05496 03125 00623 66 7 0148 223 5

09160 05208 01306 66 7 0247 168 6

1282 07292 01990 66 7 0346 13 1 2

1649 08333 01629 66 7 0445 64 93

03974 02604 00684 65 3 0097 469 7

06624 05208 02278 65 3 0162 466 5

0 9273 06250 02304 65 3 0227 290 3

1192 07292 02334 65 3 0292 177 9

09843 08854 046HO 63 6 0211 524 4

1641 13020 06346 635 0352 255 3

2297 17190 08008 636 0493bull 164 6

2953 21350 09662 63 6 0633 1 20 1


09329 03646 02760 62 7 108 174 5 1555 05208 03624 627 180 82 43 2177 06250 04010 62 7 250 46 53 2799 07292 04314 62 7 322 30 27 05441 02083 01633 63 1 0630 303 5 09068 03125 02260 63 1 106 151 2 1270 03646 02382 63 1 148 81 25 1632 04167 02497 63 1 1 90 5158 1343 04687 03341 62 6 154 101 9 2238 07812 05464 62 6 256 60 01 3134 10940 07586 62 6 358 42 50 4029 13020 08664 62 6 461 29 37


05496 04687 02185 66 7 0282 392 0

09160 06771 2869 65 7 0469 185 3

1 282 09375 04073 66 7 0658 134 3

1649 11980 05276 66 7 0846 105 2

03974 03646 01726 65 3 0 195 592 2

06624 05729 02799 65 3 0329 345 8

09273 07812 03866 65 3 0454 243 6

1192 09375 04417 65 3 0584 168 5

09843 09375 04164 63 6 0422 291 5

73

(1) (2) (3) (4) ( 5) (6)

1641 15100 08426 63 6 0704 169 6

2297 20310 11128 63 6 0986 114 3

2953 23440 11752 63 6 127 73 07


09329 03125 02239 62 7 215 70 75

1555 05729 04145 62 7 360 47 13

2177 06250 04010 62 7 502 23 27

2799 06771 03793 62 7 644 13 32

05441 01562 01112 62 8 124 103 3

09068 03125 02260 62 8 208 75 62

1270 03646 0238 0 62 8 291 40 62

1632 03646 01976 62 8 374 20 40

1343 05729 04383 62 7 308 66 81

2238 07812 05464 62 7 512 30 00

3134 09896 06552 62 7 716 18 35

4029 10940 06584 62 7 922 11 16


05497 05208 02706 66 7 0594 242 6

09160 08333 04431 66 7 0988 143 1

1282 09896 04594 66 7 138 75 71

1649 11460 04756 66 7 178 47 40


0 9329 05729 04843 62 7 322 102 0

1555 07812 06228 62 7 538 47 21

2177 08854 0661 4 62 7 755 25 58

2799 09896 06918 62 7 967 1 6 19

1343 07292 05946 62 7 462 60 42

2238 11460 09112 62 7 768 33 35

3134 13540 10 186 62 7 1 074 19 02

4029 14580 10224 62 7 1 383 11 55


05497 06250 03748 66 7 0 891 224 2

09160 09375 05473 66 7 148 117 8

1~82 10940 05638 66 7 208 6195

1649 13540 06836 66 7 267 45 41

03974 05729 03809 65 3 0585 435 7

74

(1) (2) (3) (4) ( 5) (6)

06624 07812 04882 65 3 0972 201 0 09273 09896 05950 65 3 136 1250 1192 13540 08582 65 3 175 1091


09329 03646 02760 62 7 0537 261 7

1555 05729 04145 62 7 0 3 95 1414

2177 07812 05572 62 7 125 96 98

2799 08854 05876 62 7 161 61 89

05441 01042 00572 63 0 0310 1650 09068 02083 01218 63 0 0520 1222 1270 04167 02903 63 0 0728 1485 1632 04687 03017 63 0 0935 93 45 1343 05208 03862 62 7 0770 176 6 2238 08333 05985 62 7 128 98 55 3134 11460 08106 62 7 178 68 11 4029 13540 09184 62 7 230 46 69


05497 04687 02185 66 7 0148 588 0

091 60 072pound2 03390 66 7 0247 328 4

1282 09375 04073 66 7 0346 2014

1649 10420 03716 667 0445 1111

03974 04167 02247 65 3 0097 1157

06624 05208 02278 65 3 0162 422 0

09273 07292 03346 65 3 0227 316 3

1192 08333 03375 65 3 0292 1930

09843 09396 05732 63 6 0211 480 8 1641 16 1 50 09476 63 6 0352 286 0 2297 22400 13218 63 6 0493 203 7 2953 26560 11688 63 6 0633 1387


09329 05208 04322 62 7 108 204 9

1555 07292 05708 62 7 180 97 37

2177 08854 06614 62 7 250 57 56

2799 10420 07442 62 7 322 39 20 05441 02083 01633 63 0 062 227 6 0~068 04167 03302 63 0 104 165 7 1270 05208 03944 63 0 146 100 9 1632 06250 04580 63 0 187 70 95

75

( 1 ) ( 2 ) (3) ( 4 ( 5 ) ( 6)

1343 06250 04904 62 7 154 112 1

2238 09375 07027 62 7 256 57 88

3134 12500 09146 62 7 358 38 41

4029 1354 09184 62 7 461 23 34


05497 05208 02706 66 7 0297 363 9

09160 08333 04431 66 7 0494 214 6

1282 09896 04594 66 7 0692 113 6

1649 12500 05796 66 7 0 8 90 86 63 03974 03646 01726 65 3 0195 444 2 06624 06250 03320 65 3 0324 307 5 09273 08333 04307 65 3 0454 207 3 1192 1146 06502 65 3 0584 186 0 09843 10420 06256 63 6 0422 262 3 1641 16670 09996 6~$ 6 0704 150 8 2297 22920 13738 63 6 0986 105 8


09329 bull05208 04322 62 7 21 5 102 4

1555 062f0 04666 62 7 360 39 79

2177 08333 06093 62 7 502 26 51

2799 10420 07442 62 7 644 19 60

05441 03125 02675 63 0 124 186 4

09068 04167 03302 63 0 208 82 84

1270 05208 03944 63 0 292 50 43

1632 05729 04059 63 0 374 31 4 4

1343 06250 04904 62 7 308 56 06 ~ 2238 09375 07027 62 7 51 2 28 94 3134 12500 09146 62 7 716 19 20 4029 13020 08664 62 7 922 11 01


05497 06771 04269 66 2 0 576 287 1

09160 09896 05994 66 2 0960 145 2

1282 13020 07718 66 2 134 95 39

1649 14580 07876 66 2 173 58 86


09329 06250 05364 62 7 322 84 77

1555 09375 07791 62 7 538 44 3 1

76

(1)

2177

2799

1 343

2238

3134

( 2 )

10420

1 2500

08330

13540

17710

( 3 )

08180

09522

06984

11192

14356

(4)

62 7 62 7 62 7 62 7 62 7

( 5 )

7 55

967

462

768 1 074

(6 )

2374 1672 53 25 30 73 20 10


05497

09160

1282

1 649

03974

06624

09273

1192

07812

11460

14580

17190

04687

08333

10940

14580

05310

07558

09278

104

02767

05403

06994

09622

66 2 66 2 66 2 66 2 65 3 65 3 65 3 65 3

0864

144

202

259

0585

0972

136

175

238 1 122 0

76 46 52 25

237 4 166 8 110 2

91 74

77

( 1)

Velocity

09329

1555

2177

2799

05441

09068

1270

1632

1343

2238

3134

402~

05496

09160

1282 bull1649 0 9843 1641 2297 2953

09329

1555

2177

2799

05441

09068

1270

1632

1343

TA BLE IV


(2) (3) (4) 5) 6)



02083 01038 62 4 212 24 60

03125 01276 62 4 353 1088

0468 7 02075 62 4 494 9 03

06250 02794 62 4 634 736

01562 01021 63 1 126 7114

02083 01067 63 1 211 26 77

03125 01650 63 1 295 21 09

04167 02225 63 1 379 1 7 25

03125 01552 62 7 308 1774

05208 02482 62 7 512 10 22

07292 03408 62 7 716 7 16

08333 03296 62 7 922 4 19


03125 0041 2 65 8 0563 27 71

04687 00433 65 8 0936 1049

06250 00455 65 8 - ~2-

__ 3bull54 0781 2 00474 65 8 168 06771 02176 64 2 0885 45 63 10420 03027 64 2 147 22 84 13540 03352 64 2 207 1292 177 1 04729 64 2 265 1102


02083 00559 62 4 848 1325

03125 00429 62 4 1412 4 08

04167 0044 1 62 4 1976 192

05208 00318 62 4 2 536 0 84

01042 00238 64 0 516 1659

01562 00108 64 0 865 2 72

02083 64 0 1212

03 125 00394 64 0 1 560 3 06

02083 62 7 1232

73

(1) (2 ) ( 3 ) (4) (5 ) (6)

2238 04167 00306 62 7 2 048 1 26

3134 06250 00776 62 7 2 864 1 63

4029 07292 00211 62 7 3 688 27


05496 03125 65 8 255

09160 04167 65 8 374

1282 06250 65 8 524

1649 07292 65 8 672

09843 06250 00362 64 2 354 7 59

1641 09375 64 2 568

2297 13540 00334 64 2 828 1 29

2953 15620 64 2 1 060


09329 03125 bull01920 62 4 424 2 2 75

1555 04687 02572 62 4 706 10 97

2177 06250 03267 62 4 98 8 7 11

2799 07292 03358 62 4 1 268 4 42

05441 02083 01452 63 1 252 50 59

09068 0 3125 01958 63 1 422 24 57

1270 04167 02480 63 1 590 1 5 86

1632 04687 02474 63 1 758 9 58

1343 04167 02367 62 7 616 13 53

2238 0625 03146 62 7 1 024 6 48

3 1 34 08333 03919 62 7 1 432 4 11

4029 10420 04701 62 7 1 844 2 98


05496 03125 00211 65 8 113 7 10

09160 05729 01122 65 8 187 13 59

1282 07812 01524 65 8 262 9 42

1649 09375 01402 65 8 336 5 24

09843 07292 02266 64 2 177 23 77

1641 12500 033B9 64 2 284 12 79

2297 17710 06516 64 2 414 12 56

2953 20830 06 556 642 530 7 64


09329 03125 01601 62 4 848 18 97

1555 04167 01521 62 4 1 412 6 49

2177 05208 01482 62 4 1 976 3 25

79

(1) (2) (3) (4) (5) ( 6)

2799 06250 01460 62 4 2 536 1 92

05441 01042 00238 64 0 516 8 29

09068 01562 00108 64 0 samp5- 1 36 middot

1270 02083 64 0 1 212

1632 03125 00394 64 0 1 560 1 53

1343 03125 00871 62 7 1 232 4 98

2238 05208 01347 62 7 2 048 2 77

0134 00333 02859 62 7 2 864 3 00

4029 09375 02294 62 7 3 688 1 46


05496 03646 00298 65 8 225 10 02 09160 05208 65 8 374 1282 07292 - 65 8 524 1649 08333 65 8 672 09843 0 6 771 00883 64 2 354 9 25 1641 10 420 64 2 568 -shy 2297 15620 02414 64 2 828 4 65


09329 03646 bull 02122 62 4 8 48 12 58

1555 05208 02562 62 4 1 412 5 46

2177 07292 03566 62 4 1 976 3 88

2799 08333 03443 62 4 2 536 2 27 05441 02083 01279 64 0 51 6 22 28 09068 03125 01671 64 0 865 10 48 1270 03646 01557 64 0 1212 4 98 1632 04167 0 1 436 64 0 1560 2 78 1343 05208 02954 62 7 1 232 8 45 2238 08333 04472 62 7 2 048 4 60 3134 1146 05986 62 7 2 864 3 15 4029 1354 06459 62 7 3 588 2 05


05496 05729 02381 65 8 225 40 05

09160 07812 02500 65 8 374 1 5 14

1282 09896 02621 65 8 524 8 10

1649 11980 02738 65 8 672 4 74

03974 03646 0108 7 65 3 156 34 98 06624 06771 02776 65 3 260 32 15 09273 08333 028 96 65 3 363 1710 1192 12500 05625 65 3 468 20 11

80

(1) ( 2 (3 ) (4) ( 5 ) (6)

0 pound1843 09375 03487 64 2 354 18 28

1641 1615 06602 64 2 568 12 46

2297 2292 09714 64 2 828 9 35


09329 05208 03056 62 4 1 696 9 05

1555 07292 03584 62 4 2 824 3 82

21 77 09375 04163 62 4 3 952 2 26

2799 10420 03618 62 4 5 072 1 bull 19

05441 02604 01430 63 1 1 008 1 2 46

09068 04167 02094 63 1 1 688 6 57

1270 05729 02773 63 1 2 360 4 43

1632 06250 02407 63 1 3 032 2 33

1343 06250 03088 62 7 2 464 4 4 1

2238 10420 05046 62 7 4 096 2 60

3134 13540 05946 62 7 5 728 1 56

4029 15620 05814 62 7 7 376 92


05496 05208 01014 65 8 45 8 52

09160 08333 01611 65 8 149 4 88

1282 11460 02212 65 8 1 048 3 42

1649 1354 01760 65 8 1 344 1 65

03974 05208 02010 65 3 312 32 34

06624 07292 02232 65 3 520 12 92

09273 08854 01926 65 3 726 5 69

1192 1250 03708 65 3 935 6 63

09843 1250 04888 64 2 708 12 81

1 641 20830 08408 64 2 1 136 6 46

2297 26040 08810 64 2 1 656 4 24

2953 30210 08178 64 2 2 120 2 38


09329 05729 04205 62 4 848 12 46

1555 08854 06208 62 4 1 412 6 62

2177 10940 07214 62 4 1 976 3 92

2799 11980 07090 62 4 2 536 2 33 05441 02604 01800 64 0 516 15 69 09068 04687 03233 64 0 865 10 14 1270 05729 03640 64 0 1 212 5 82 1632 0625 03519 64 0 1 560 3 41 1343 06771 04517 62 7 1 232 6 45

81

(1) 2) 3) ( 4) (5) (6)

2238 11980 08119 62 7 2 048 4 18

3134 1615 10676 62 7 2 064 2 80

4029 2031 13229 62 7 3 688 2 10


05496 07812 04464 65 8 225 37 53

09160 11980 06668 65 8 374 20 19

1282 14060 06785 65 8 524 10 48

1649 15620 06378 65 8 672 5 96

03974 05729 03072 63 5 135 49 40

06624 08854 04695 63 5 225 27 17

09273 11980 06314 63 5 315 18 66

1192 15100 08931 63 5 405 1 5 97

09843 1 5100 08712 64 2 354 22 84

1641 22400 12852 64 2 568 12 10

2297 28650 15444 64 2 828 7 43

82

TABLE l


(1) (2) (3) (4) (5) (6)



09329 07812 06040 62 9 432 71 60

1555 13020 09852 62 9 720 42 03

217 16150 11630 62 9 1 010 25 31

2799 17180 11224 62 9 1 296 14 78

05441 04687 03787 63 6 255 131 9

09068 06771 05059 63 6 428 63 47

1270 08854 05326 63 6 599 40 46

1632 10940 07600 636 770 29 43

1343 11980 09288 62 7 616 53 11

2238 19270 14574 62 7 1 024 30 01

3 134 25520 18812 62 7 1432 19 76


05496 11980 06976 65 7 113 234 7

09160 18230 10426 65 7 187 126 3

1282 25000 14396 65 7 262 88 98

1649 30730 17322 65 7 336 64 73

03974 10420 06580 63 5 0676 423 5

06624 15620 09760 63 5 112 226 0

09273 20830 12938 635 157 152 9

1192 25000 15084 63 5 202 107 8

09843 21870 13542 64 2 177 1 42 0

1641 35420 22072 64 2 294 83 28

2297 42710 24346 642 414 46 89


0 9329 06250 04478 62 6 319 94 37

1555 09896 06728 62 6 532 51 01

2177 13020 08540 62 6 745 33 04

2799 15620 09664 62 6 960 2262

05441 03646 02746 63 1 188 170 1

09068 06250 04538 631 315 101 2

1270 07812 05284 63 1 441 60 06

83

(1) (2) (3) (4 ) (5) (6)

1632 08854 05514 63 1 566 37 97

1343 07812 05120 62 7 462 52 04

2238 14060 09364 62 7 768 34 28

3134 20310 13602 62 7 1 074 25 39


05496 09375 04371 65 6 0825 261 3

09160 1458 0 06776 65 6 1 38 145 9

1282 1 8230 07626 65 6 192 83 79

1649 23960 10552 65 6 248 70 10

03974 06771 02931 63 5 0507 335 4

06624 11980 06120 63 5 0843 252 0

09273 15100 07208 63 5 118 151 4

1192 20310 10394 63 5 152 1321

09843 16670 08342 64 2 133 1 5 5 5

1641 27080 13732 64 2 221 85 39

2297 35420 17056 64 2 310 5840


09329 04167 02395 62 6 213 1135

1555 07292 04124 62 6 355 70 34

2177 09375 04895 62 6 497 42 62

2799 10420 04464 62 6 640 23 51

05441 02083 01183 63 1 125 164 9

09068 03125 01413 63 1 210 70 91

1270 04167 01639 63 1 294 41 92

1632 05208 01868 63 1 377 28 93

1343 05208 02516 62 7 308 57 52

2238 08333 03637 62 7 512 29 95

3134 11980 05272 62 7 716 22 15

4029 14580 05868 62 7 922 14 91


bull05496 06250 01246 65 6 0550 167 6 09160 098 96 02092 65 6 0918 101 3 1282 13020 02416 65 6 128 5972 1649 16150 02742 6 5 6 165 4096 03974 04687 00 8 47 63 5 0338 218 0 06624 07812 01952 63 5 0562 180 8 09273 10940 03048 63 5 0788 144 1 1192 1 3 020 03104 63 5 101 88 77 0 9843 1250 04172 64 2 0885 174 9

84

(1) (2) (3) (4 (5) (6)

1641 20830 07482 64 2 147 112 9

2297 27080 08716 64 2 207 67 13

2953 33330 09954 64 2 265 46 4


09329 02083 00311 62 6 107 58 99

1555 04167 00999 62 6 178 68 17

2177 06250 01770 62 6 249 61 64

2799 07292 01336 62 6 320 28 15

05441 01042 00142 63 1 0628 7918

09068 02083 00371 63 1 105 74 48

1270 03125 00597 63 1 147 61 09

1632 04167 00827 63 1 188 5125

1343 03125 00433 62 7 154 39 62

2238 05208 00512 62 7 256 1686

3134 07812 01104 62 7 358 1924

4029 09375 00663 62 7 461 6 99


09329 14580 12808 62 6 852 7601

1555 20830 17762 62 6 1420 37 88

2177 23960 19480 62 6 1988 21 20

2799 28120 22164 62 6 2 560 1459

05441 07292 06392 63 2 508 1114

09068 1198 10268 63 2 852 64 40

1270 15620 13092 63 2 1192 41 86 1632 18230 14890 63 2 1532 28 83 1343 1979 17098 62 7 1232 48 87 2238 30210 25514 62 7 2 048 26 27


05496 19790 14786 65 6 220 248 7

09160 31250 23446 65 6 367 1420

1282 41 670 31066 65 6 514 96 01

03974 16150 12310 63 5 135 396 1

06624 23440 17580 63 5 225 203 6

09273 31770 23878 63 5 31 5 1411


09329 08333 06561 62 9 648 69 13

1555 12500 09332 62 6 1070 35 38

2177 17710 13230 62 6 1498 25 59

8 5

(1) (2 ) ( 3) (4) (5 ) ( 6)

2799 18750 12794 62 6 1 944 14 98

05441 05208 04308 63 6 383 133 4

09068 07292 05580 63 6 642 62 23

1270 09375 06847 63 6 899 38 92

1632 10420 07080 63 6 1 155 24 37

1343 12500 09808 62 7 924 49 84

2238 18750 14054 62 7 1 536 25 72

3134 25000 18292 62 7 2 148 17 08


05496 12500 07504 65 6 165 224 3 09160 17710 09906 65 6 275 106 6 1282 23960 13356 65 6 385 73 38 1649 31250 17842 65 6 495 59 26 03974 10420 06580 63 5 101 376 4 06624 15620 09760 63 5 169 200 9 09273 21350 13458 63 5 236 141 4 1192 26040 16124 63 5 303 102 5 09843 22920 14592 64 2 266 136 0 1641 37510 24152 64 2 441 810


09329 04687 0291 5 62 9 432 69 10

1555 0781 2 04644 62 9 720 39 61

2177 09896 05416 62 9 1 010 23 57

2799 10940 04984 62 9 1296 13 12

05441 02604 0 1704 63 6 255 118 7

09068 03646 01934 63 6 428 48 52

1270 04687 02159 63 6 599 27 60

1632 05729 02389 63 6 770 18 50

1343 06771 04079 62 7 616 46 63

2238 10940 06244 62 7 1 024 25 72

3134 16150 09442 62 7 1 432 19 83

4029 19270 10558 62 7 1 844 1 3 42


05496 08333 03329 65 7 113 223 9

09160 11980 04176 65 7 1 87 101 1

1 282 15100 04496 65 7 262 55 56

1649 18230 04822 65 7 336 36 03

03974 05729 01889 63 5 0676 243 1

06624 10420 04560 63 5 112 211 1

86

(1) (2) (3) (4 (5) (6)

09273 14580 06688 63 5 157 158 0

1192 17710 07794 63 5 202 1114

09843 15620 07292 64 2 177 1 52 9

1641 25000 11652 64 2 294 87 91

2297 31250 12886 64 2 414 49 64


09329 03 125 0 1353 62 6 21 3 1283

1555 05208 02040 62 6 355 69 60

2177 07292 0281 2 62 6 497 48 95

2799 08333 02377 62 6 640 25 04

05441 01042 00142 63 2 127 39 54

09068 02083 00371 63 2 bull 213 37 24

1270 03125 00597 63 2 298 30 54

1632 04167 00827 63 2 383 25 62

1343 04467 01475 62 7 308 67 46

2238 06771 02075 62 7 512 34 18

3134 09375 02667 62 7 716 22 40 4029 11460 02748 627 922 1397


05496 05208 00204 65 6 055 54 88

09160 07292 65 6 0918

1282

03974 10420 03646 -shy 65 6

63 5 128 0338 -shy

06624

09273 06250 07292

00390-shy 63 5 63 5

0562

0788 72 21-shy 09843 09375 01843 64 2 0885 87 47

1641 16150 02802 64 2 147 84 59

2297 21870 03506 64 2 207 54 02

2953 26040 02664 64 2 265 24 84


09329 07292 05520 62 6 852 65 44

1555 12500 09332 62 6 1420 39 80

2177 15620 11140 62 6 1988 24 25

2799 16670 10714 62 6 2 560 1411

05441 04167 03267 63 2 508 1139

09068 06771 05059 63 2 852 63 47

1270 08333 05805 63 2 1 192 37 12

1632 09375 06035 63 2 1532 23 38

1343 10420 07728 62 7 1232 44 19

2238 16670 11974 62 7 2 048 24 66

3134 22920 16212 62 7 2 864 1703

87

( l) (2 (3) (4) ( 5) (6)


bull 05496 10940 05936 65 6 220 199 6 09160 16150 08346 65 6 367 1011 1282 21350 10746 65 6 514 66~41 1649 28650 15242 65 6 660 56 96 03974 08854 05014 63 5 135 3227 06624 13020 07160 63 5 225 165 8 09273 17190 -09298 63 5 315 1100 1192 21350 11434 63 5 404 81 76 09843 21350 13022 64 2 354 1365 1641 3281 19462 64 2 588 7343 2297 40100 21736 64 2 828 41 8 7


09329 05208 03436 62 9 648 7240

1555 08333 05165 62 9 1 080 39 17 - 2177 10420 0 5940 62 9 1 515 22 98 2799 11460 05504 62 9 1944 12 88 05441 03125 02225 63 6 383 137 8 09068 05208 03496 63 6 642 77 97 1270 06250 03722 63 6 899 42 31 1632 06771 03431 63 6 1155 23 61 1343 07292 04600 62 7 924 46 75 2238 12500 07804 62 7 1 536 28 57 3134 16670 09962 62 7 2 148 18 61


05496 08333 03329 65 6 165 224 3

09160 12500 04696 65 6 275 101 1

1282 16670 06066 65 6 385 66 66

1649 19790 06382 65 6 495 42 40

03974 06771 02931 63 5 101 335 4

06624 09896 04036 63 5 169 166 1

09273 13540 05648 63 5 236 118 7

1192 16670 06759 63 5 303 85 66

09843 15600 07272 64 2 266 135 6

164 1 25000 11652 64 2 441 7815 2297 33330 14966 64 2 621 51 25


09329 04167 02395 62 6 426 113 5

1555 06250 03082 62 6 710 52 59

88

(1) (2) ( 3 ) (4) ( 5) (6)

2177 09375 04895 62 6 994 42 62

2799 10420 04464 62 6 1 280 23 51

05441 02083 01183 63 2 254 164 9

09068 02604 00892 63 2 426 44 76

1270 04167 01639 63 2 596 41 92

1632 05208 01868 63 2 766 28 93

1343 04687 01 995 62 7 616 45 61

2238 08854 04158 62 7 1 024 34 25

3134 11980 05272 62 7 1 432 22 15

4029 14060 05348 62 7 1 844 1359


05496 05729 00725 65 6 110 97 52

0 9160 09375 01571 65 6 184 76 10

1282 11980 01376 65 6 257 34 00

1649 14580 01172 65 6 330 17 52

03974 05729 01889 63 5 0676 486 3

06624 0781 2 01952 63 5 112 180 8

09273 09896 02004 63 5 157 94 5

1192 10940 01034 63 5 202 29 57

0 9843 11460 03132 64 2 177 131 4

1641 17710 04362 64 2 294 65 82

2297 24480 06116 64 2 414 47 12

2953 30730 07354 64 2 530 34 28


09329 03125 01353 62 6 213 256 6

1555 04167 00999 62 6 355 68 17

2177 05208 00728 62 6 497 25 35

2799 06250 00294 62 6 640 6 19

05441 01042 00142 62 9 125 7 9 18

09068 02083 00371 62 9 210 74 48

1270 03125 00597 62 9 294 61 09

1632 04167 00827 62 9 377 51 25

1343 03125 00433 62 7 308 39 62

2238 05208 00512 62 7 512 16 86

3134 07292 00584 62 7 716 9 81

4029 08333 62 7 922

89


TABLE VI



Light oil SAE 140)

60 0 56 2 61 4 56 2 63 6 56 1 65 8 56 0

Heavy oil (SAE 250)

63 4 57 0 65 8 57 0 66 7 56 9

90






FIGURE 18


H

- ~ -ii li






FIGURE 19

92









Reynolds number shy


ft3 ft-sec



ft





o ol29 lbf

93


for F ow)











( 56 1 lb curt) (0 09329 ft sec ) 2 (001389 ft 2 ) m

113 5



94




Length - 0 0833 ft





3 2(0 09329 ft sec )0 0833 ft)(2 06 l b m) = 0 00159 lb



0 02083 lb - 0 00886 lb - 0 00159 lb = 0 01038 l b


24 6

Documents

Drag Coefficients for Flat Plates, Spheres, and Cylinders