HM 122 Fluid Friction Loss Measuring System

Theoretcal principles

Pipe flow with friction

4

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Below, the purpose is to determne the calculationofpressure loss pv and loss level hv in pipe flowwith f riction.ln the case of turbulant pipe flow, it is regardedas formed with a Reynolds number Re>2320 if thepressure loss s proportional to the- length I of ppe- pipe friction coefficient )"- Density p of the ftow medum- square of the flow velocity v.The pressure loss also increases as the pipe dia-meter is reduced. lt is calculated as follows

"tPv=23 P v' .

The associated loss level hv is calculated as fol_Iows

n-il "

""- d 29.ln the case of turbulent pipe ftow( Re>2320) thepipe frction coefficient " depends on the pperoughness k and the Reynolds,s number Re. The piperoughness k defines the height of the wall elevatons inmm. The roughness of the experiment ppes s lisied inthe Appendix in a table. The relatonship beh/een Re,}"and kisshown in the diagram according to Colebrookand Nkuradse. Here, the wall roughness k is re_ferred to the ppe diameter d.

4 Theoretical principles Ib

HM'122 Fluid Friction Loss Measuring System

Fig, 4.1 Pipe friction number , accordng to Colebrook and (dotted) Nikuradse(from Dubbel: Manual of Mechanical Engineering)

.?0

300

100120

200

5

00200.0i 800160.0110 012

0olo0,0090.0080.007

000I011

2000

5000r0C002000050000

t00 000

The Eeynold's number Fle s calculatd f rom thepipe diameter d, the flow velocty v and the kine-matic viscosity v.

Re='d.v

The kinematic viscosty can be found in Table 6.2.1for water as a functon of the temperature.The llow velocity v is calculated f rom the volume-tric f low V and the pipe cross section.

4vV =__ -n d'

For hydraulically smooth pipes (Re < 65 d/k)and a Reynold's number in the range of 2320< Re< 105, the pipe friction coeff icient is calculated inaccordance with the formula of Blasius.

" 0.3164

ri Re

b

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-

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II,9,

4 Theoretical prnciples 17

HM 122 Ftuid Friction Loss Measuring System ffi

For pipes in lhe transition range to rough ppes(65 d/k < Re < 1300 d/k, range in the diagrambelow the limit curve), the ppe f ricton coeffcentis calculated according to Colebrook

x:f zn( 2'51-+0?7 \1'" L-',IRe,' drL rr\'- " '" )"It is an implict formula which must be solved iterati-vely. First estimate ), , insert it into the formula andcalculate the first approximation. This approximationis inserted back nto the equaton and a secondapproximation is calcuated.lf the estimated value is taken from the diagramaccording to Colebrook and Nikuradse, the frstapproximation generally already has suffcient ac-curacy and the values differ only in the third deci-mal place.

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Resistance coefficient of special pipeline elements

Specal pipeline elements and fttings such as pipebends or elbows, ppe branches, cross sectionchanges or also valves and flaps create additionalpressure losses in addition to the wall f riction los-

In the case of cross section changes and there-fore associated speed changes, components fromthe Bernoulli pressureoss (dyn. pressure) mustalso be taken into account in the total pressure loss.The Bernoul equation lvith loss element is

o v? n r3i * p., + p 9 zt =' z1 * pr+ p g22+^pv.

I

4 Theoretical prnciples 18

HM 122 Fluid Friction Loss Measuring System

Assumng equal levels 21 and 22, this gives themeasurable total pressure loss

Aps"" -

pr -

pz=P2 qv!-vl, +tp, .

The followng is obtained for the loss level

hro"" = ,'., 1vr'-vi) +h, .

Apart f rom a few special cases, the additional flowresistances cannot be calculated in a systematicway, in contrast to the wall f riction losses inves-tigated in the previous section.

Empirically obtained resistance coefficients( arequoted here in the literature for the various ele-ments. These alow the additional pressure lossesto be calculated easily

- v'P-- \P 2

or for the loss levels

. .- v2n'z: qZ g'

The followng can thereby written for the total losslevel

1 "

, )., l,vl xrl ,vf -v!h,n..=-2b tv2'-vt'\ 1 2S d;* g' r*(" r',

The ppe frction resistance must be determnedseparately for the section before and after thecross section change. ln contrast, the resistancecoefficient is only referred to the velocity v2 afterthe cross section change.

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4 Theoretical principles

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ffiffitr

HM 122 Fluid Friction Loss Measuring System

=

3trd

=

aIadadaddd

--dd-

=aJdI

a-d-4EE-d-dEIraEJ

4.2,1 Pipe bend

R

HM 122 Fluid Friction Loss Measuring System

-"--nI'?n--l

Snrooth

+tgRato of the bend radus to the ppe diameier B/d

Fig. 4 3 Resistance coefficient ( as a function of the radius ratio B/dCross secton changes

O,B

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.9

3,0.2fI

10

e

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The cross sectionchanges in the test rjg are conti_nuous wdenings or narrowings in each case" In thecase of a contnuous cross secton change, theresistance coefficent can be found in special da_grams (Section 6.2.3).For a discontnuous cross section change, theresistance coefficient can be derived from the Ber_noulli equation and the pulse set.The followng applies to the Wdening

F9.4.4

Narrowing of theflow cross section

Cross sectlonchange

,=[^+-,j [.s ,lfollowing accordingly applles to the narro_The

wing

,=[^1-,1=[# ,J

4 Theoretical princjples t

HM 122 Fluid Friction Loss Measuring System

=

=

a

I=

=

a

=

-

J

e3f,d

=

-

-arJ

-

d

-d

-

-ldJ

-

{

-J

Here, Aoand do is the reduced cross section. Sncethis s normally unknown, we refer to the followingdiagram for the resistance coefficient in the caseof narrowing.

0.6

0.4

o.2

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=IiE(,

E 4.3(5izioI6II3

0

Fig.4.5

4.2 0.4 0 6surface ratio A2lA1

08

Resistance coefiicient ( in the case ofdiscontjnuous narrowing

Fig.4.6

Resstance coefficient of pipelne tittngs

Needle valve

Slide valveShut-off organs

Depending on the design, pipeline fttings result invarying losses. However, a certain function js a jsoralized with the types shown in Fig. 4.6 ad 4.7.As a result, a needle valve results in a very hghpressure loss due to the marked cross sectionnarrowing and the diversion of two x 90". However,for this, the design permits very fine adjustment ofthe flow.

Very low losses ((n . O.S on the other hand occurwhen a slide valve is used. The fluid can flowthrough the valve almost unhndered_ However,the slide valve frees a Iarge cross section even witha very small opening, so that hardly any regulationis possible.The straight seat valve and the slanted seatvalve have a significantly higher resistance coef-

4 Theoretical princjp,es

Slraight seat val-

Slanted seat valve

Flg.4.7

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HM 122 Ftuid Friction Loss Measuring system ffi

fcient due to the fissured penetration cross sec-tion. However, the slanted seatvalve is significant-ly more favorable as regards flow than a standardstraght seat valve conformng to DlN, since theflow s not dverted so much. While a resstancecoefficient of approximately (n = S.O must be ex-pected in the case of the straight seat valve,eR - 1.5-2.0 can be assumed in the case of asanted seat valve. Both valves permit condtionaladjustment of the flow. The slanted seat valvenormally requires more installaton space. The ballvalve has a completely smooth and free penetra-tion cross section when opened. This means thatvery low pressure losses can be expected with it.Resstance coeffcients of as low as (n : 0.03 canbe obtained. It even allows very good adjustmentof the volumetric flow.

Shut-off organs

Calculation of the resistance coefficient

The resistance coefficients are determned on thebasis of the following formula for the valves

" 2h"...9

^ |gn: v2--^d'The distance between the measuring glands isused as the length I

Opening characterstics of shut-off organs

f shut-off organs are used for adiusting cerlainvolumetrc flows in pipeline systems, great valuemust be placed on good metering capablity espe-cially when opening degrees are limited.

4 Theoretical principles 23

HM 122 Fluid Friction Loss Measuring System

II=

a

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a-rl

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=

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F9.4.8 Open,ng characterisiics o,shutolf organs

Pitot tube

A progressve characterstic is the optimum here,with whch the opening degree increases at firstslowly and then more and more quckly. ln thiscase, adjustment of the shut-off organ by a definedabsolute amount results in a correspondng per_centage change of the volumetric flow.For example:A valve with a maximum opening of 1 O revolutionss opened from 1 to 2 revolutions, in other words10% absolute, then the volumetric flow will ncrea-se reatively by 1O%, e.g. from 1 to 1.1 /min.This so-called "equal percentage', characteristic isshown with the progressive in the dagram oppo-site. Next to t is a linear and degressive charac_teristc, of the type whch occurs with typicalshut-off organs.

Both the static pressure and the total pressure aremeasured with the ptot tube. The difference be_tween these two values gives the dynamic pressu-re pdyn-

Payn=Pges-Pstat

The dynamic pressure is proportional to the squareof the flow velocity and can be calcujated as fol_lows:

PaY' = 9r' v2

p: Specific density of water

4 Theoretical principles 24

HM 122 Fluid Friction Loss Measuring System EgI

Resistance coeffcents of specal ppeline elements

Method

Connect the double manometer to the measuringglands of the pipeline elements being measuredand perform the measurements as outllned inChapter 2.5. Note the displays of the double ma-nometer or the differential pressure sensor andflow meter. The pressure losses at each elementand any combinations can be recorded via the ringchambers. They are always installed in the sectionwith the same measurement length, so that theresults can be directly compared with each other.The measuring section is made up of a the follo-wing elements:- 1 : angle 90', R=12mm, di=16 mm, Cu- 2: angle 90", R=12mm, d=16 mm, Cu- 3: angle 90', B=1 2mm, d=16 mm, Cu- 4: bend 90., R=22 mm, di=16 mm, Cu- 5: long bend 90", R=28 mm, di=16 mm, Gu- 6'.2x bend 45', d=16 mm, Cu- 7: reducing sleeve 18-15, Cu- 8: reducng sleeve 15- 18, Cu- 9: angle 9O', Ft=15 mm, d=19 mm, SVZn- 10: angle 9O', R=15 mm, di=1 9 mm, SVZn- 11: angle 90', R=15 mm, di=19 mm, SVZn-

'12: bend 90', R=32 mm, di=19 mm, SVZn- 13: long bend 9O', R-42 mm, di=1 9 mm, St/Zn

5.2

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Fig. 5.3 l\leasuring section. pipeline elements

5 Experiments

HM 122 Ftuid Friction Loss Measuring System

,- 2hvgesg . I'----.--^d'

The pipe tength between the measurng gtandsreferred to the ppe center lne is used for j _

a

(,e2

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Calcuaiion variables for (The following is obtained f rom the caleulation va-rables:

e ("2")= t -z+e U")=o.t+

Both resistance coefficents are above the figuresquoted in the literature (rough pipe knee for theangle: (rough=1 .27; in the case of a bend wthR/d=1 .375, (rough=O.4 is read off n the diagram).The deviation s due to dirty transitions betweenthe pipes and the angle or bracket.

Pressure losses of pipeline fxturesMethod

This experment is intended to record the pressurelosses of the different ppeline fXures. To do this,connect a double pressure manometer or differen_tial pressure sensorto the measurng glands oftherelevant f ixture, and carry out the measurement asoutlined n Section 2.S. The installaton of fxtures

5.3

5.3.1

5 Experiments ae

HM'122 Fluid Friction Loss Measuring System

is shown in Fig. 5.8. Note the dspays of the doublemanometers or sensors and flow meters in a table.

Needle valve slide valve straight seal valve slanted seat valve ball valve:

Fig. 5.8 lvieasurng seciion, Pipeline filtings

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The pressure loss was recorded with the valvesfully opened and therefore maximum possibleflow. The measurement results are shown in Table5.6. Their quality is n line with expectations.

Fitting pressure loss ^p

Needle valve 680 mbar

Slide valve 8 mbar

Straight seat valve 104 mbar

Slanted seat valve 18 mbar

Ball valve I mbarTab. 5.6 Pressure losses of pipeline fiiiings

5 Experiments eo