USN

Time: 3 hrs.

2a.

b.

c.

3a.

b.

1 ',u, Find the Fourier series

*2@ril \'- I

B 3(2n-1)r'

fi*.{''{,1

1OMAT31

Marks:100

,,,,,,,,

hence deduce that

,,, (06 Marks)

(07 Marks)

lMarks;

(07 Marks)

(07 Marks)

(06 Mar,Iq)

most closely to the

(07 Marks)

Third Semester B.E. Degree Examination, Dec.2013 lJan.2Dl4Engineering Mathematics - lll

Max.Note: Answer FIVEfull questions, selecting

at least TWO questions from each partPART _ A

expansion of the function f(x) = lxl in Gn,x),(JooLo.

6

o!

oL

.96

^\(.)X

J'F6NV

lFh

50"iooFl

.=N.B+

Y o.)

OieO

-'-o>a_-o=

a=LVoc)

-!

-L

ad

E6

'iaor=a-a >'1oXsdo_i6Vo=

4l!

€;LO

5.e>\ (tsao o-c or.)

o=o.Btr>=o5!

^5t<* a.I

a_)

Z

oa

b. Obtainthehalf-rangecosineseriesforthefunction, f(x)=(*-1)'intheinterval 0<x<1

ura n.n.. show that n' = r{} * } * +. } (07 Marks)u'3'5')c. Compute the constant term and first two harmonics of the Fouripr series of (x) given by,

Obtain the Fourier cosine tru for* of f(x) = -L.l+x'h- *'for lxl < I

Find the Fourier translorm of f r x) = i -

I o forlxl >t

SFind the inverse Fourier sine transform of ,;*Obtain the various possible solutions of two dimensional Laplace's equation, u,* *u,, = 0

by the method of separation of variables. (07 Marks)r2 r2. _.. o-u o-u

Solve the one-dimensional wave equation, C' j=-, 0 < x < / under the following' 6x' A',\ ,, ,\ UnX

conditions (i) u(0, t) : u(1, 0 : 0 (ii) u(x, 0) : ; where u6 is constant

(iii) ;(x.0) = 0.

c."' Obtain the D'Almbert's solution of the

u(x. 0) : (x) una $1*.0) = 0a"'

(07 Marks)

wave equation u,, - C'r** subject to the conditions

4 a. Findthe best values of a, b, c, if the equation y=a+bx+cx2 is to fitfo llo wing observations.

Solve the following by graphical method to maximize z = 50x + 60y subject to the

constraints, 2x+3y<1500, 3x+2y <1500, 0( x<400 and 0<y<400. (06Marks)

By using Simplex method, maximize P=4xr -2xr-x, subject to the constraints,

xr +x2*X: (3,2xr+2xr*X., ( 4,xt-x, <0, X,)0 and xz )0. (07Marks)

x 0 fiJ

2n.,,.

J

.,.....fi 4x;J

5n;J

2n

f(x) 1.0 r.4 1.9 1.7 ,,,1 .5 t.2 1.0 CENfRALLIBRAflY

x 1 2 -) 4 5

v 10 t2 13 t6 t9

c.

1OMAT31PART _ B

Using Newton-Raphson method, find a real root of xsin x + cosx = 0 nearer to n, carryout5a.

b.three iterations upto 4-decimals places.Find the largest eigen value and the corresponding eigen vector of the matrix,

lz -1 oll-, 2 -11

Io -r ,)By using the power method by taking the initial vector as [t t t]'

Solve the following system of equations by Relaxation method:l}x+y+z=31 ; 2x+8y-z=24; 3x+4y+l0z=58

carryout 5 -iterations.(07 Marks)

(06 Marks)

lassified below,

(07 Marks)

rule by taking 6 - equal strips and hence

(07 Marks)

(06 Marks)

(07 Marks)

c.

6 a. A

7a.

sulvey conoucteo m a slum locallty reveals tne lollowlns mlormatron as cIncome per dav in Ruoees 'x' Under 10 10 -20 20-30 30-40 40-50Numbers of persons 'y' 20 45 115 210 115

Estimate the probable number of persons in the income group 2A b 25.

diflerence formula.x 2 4 5 6 8 10

f(x) t0 96 t96 350 868 1746

nducted in a slum locali ls the followins info

. Estlmate tne pr0DaDle numDel oI persons rn tne mcome group lU to"/.5. (07 Marks)b. Determine (x) as a polynomials in x for the data given below by using the Newton's divided

c. Evaluate [. +dx by using Simpson'sjl+x H'

c.

deduce an approximate value of log. 2. (06 Marks)^ ) ^)

Solve the wave equation, + = 4+, subject to u(0, t) : 0, u(4, t) : 0, u1(x, 0) : 0 andol- dx'u(x. 0) : x(4 - x) by taking h : l. K : 0.j upto 4-steps. (07 Marks)

Solve numerically the equatio" + =* subject to the conditions. u(0. t):0: utl. t.1.'A0x'

t ) 0 and u(x,0): s.innr, 0< x <1, carryout the computation fortwo levels taking h =1l.

and K: + . (07 Marks)36

Solve u,o * u, = 0 in the following square region with the boundary conditions as

indicated in the Fig. Q7 (c). (06 Marks)

Fig. Q7 (c)

0000Find the z-transform o[ (i) sinh n0 (ii) coshnO

Find the inverse z-transform or" 222 +32' (z+2)@-a)

Solve the difference equation, y n+2 * 6y,*r * 9y , - )nwith yo = yr = 0 by using z-transform.

*rk*rk>k

tt1

?n

8a.b.

c.

500 I 00 100 50

(xr) n-

(07 Marks)

USN TOME/AU32B

Third Semester B.E. Degree Examination, Dec.2013 lJan.20l4

Mechanical Measurements and Metrology

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

at least TWO questions from each part.

PART _ Aa. De{ine metre in terms of wavelength standards. List the advantages of wavelength standards

(06 Marks)

(08 Marks)

mm longer. Determine the actual dimensions of all the four end

over itaterial standards.b. Describe with a neat sketch:

i) Imperial standard yardii) Wringing phenomena of slip gauges

c. Four length bars of basic length 100 mm are to be calibrated,using a calibrated length bar of400 mm whose actual length is 399.9992 mm. It was also found that length of bars B, C and

D in comparison to A are +0.0002 mm. +0.0004 mm and -0.0001 mm respectively and thelength of all the four bars put together in comparison to standard calibrated bar is +0.0003

c)()(.)CB

o.

(.)

(.)!

8e

6v7r'-to0'=oo.: c.l

HOO

oJtr=o

71. -

a:

oO

o0c

-€

or=

p-Ao''o_i

o=

AEG;:9v,^:-40o=qotr>Xoo

rJ<-i c.i

ooZ

L

a. Differentiate between:i) Hole basis and shaft basis system of tolerancesii) Interchangeability and selective assembly.

b. Write notes on:i) Compound tolerancesii) Gauge tolerance.

Marks)

(08 Marks)

(06 Marks)

(06 Marks)

(06 Marks)(08 Marks)(06 Marks)

3a.b.c.

(08 Marks)

(08 Marks)(08 Marks)

Show the arrangement of angle gauges, with a neat sketch by selecting minimum number ofgauges for the angles 32'15'33" and54o36'42". ',,. (04 Marks)

4 a. What is the best size wire? Derive an expression for the same in terms of the pitch and angle, of the thread.

b. Explain 3-wire method of measuring effective diameter of screw thread.c. Explain the principle of interferrometry. Write a note on optical flat.

PART - B5 a. With a neat block diagram, explain the generalized measurement system with an example to

c. Determine the dimensions of hole and shaft for a fit 30H8f7. The given data arc:i:0.45Dr/r + 0.001D. IT8 :25i.1T7: l6i. Fundamentaldeviation for shaft'f is -5.5D0+r.30 mm diameter lies in the diameter step of 18-30 mm. Sketch the fit and comment on thesame.

Explain with a neat sketch, the working of Solex pneumatic gauge,Explain with a neat sketch, the construction and working of LVDT.

each stage.

b. Distinguish between: i) Primary and secondary transducersii) Active and passive transducers

c. Define the following terms with reference to measurement system:i) Calibrationiii) Hysterisis

ii) Sensitivityiv) Threshold value

..

t,,r,,:,r,

1.t)

2 of2

USN

Advanced Mathematics - I

Time: 3 hrs.

,:.,i , Note: Answer any FIVEfull questions.

1 ' ;. Express the complex number (1 + i)(1 + 3i)

in the form x + iy.1+ 5i

MATDIP3Ol

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

(07 Marks)

(07 Marks)

Third Semester B.E. Degree Examination, Dec.2013 /Jan.20l4

Max. Marks:100

,'

..,"'.'.,......,'..

(06 Marks)dooLa

oC)

oXd=

=hj

boltroo.=N

o:uotraO

o2

a:

o(.)

botr

-?oOE

o-A

oj

o=aoatE

!O

5.Y>'!uoviouo=o. litr>=o5L

\J<-Noo

'7

Loo.

b.

c.

2a.b.

c.

a.

b.

c.

4a.

b.

c.

5a.

b.

c.

6a.

b.

c.

r ----.-,:---r- -. (3- J 'Find the modulus and amplitude of trExpand coso 0 in a series of cosines multiples of 0.

Find the nth deiivative of sin(ax + b).

If y: (sin-l x)2, Showthat (1-x')y,*, -(2n+l)xy,*, -n'.yn=fl

^[ r -3t2 IFindthenthderivativeof I +,. i'- l.[51x-ll (?-tf2x+3)J

Using Taylor's theorem, express the polynomial 2xr +7x2 +x - 6 in powers of (x - 1).(06 Marks)

Using Maclaurin's series. expand tan x upto the term containing "t.r'6 Y (07 Marks)usmg .vtaclaurrn's senes, expand ran x upto rhe term contammg x;,3\g;:{gN(0, Marks)

lf z =r' + y'' - 3axy then prove ,1'ru, 9'l = :t: ''^y \c)\

ovox axav iY

"Er.r{E&t \Sqi

Marks)- "-"- AyAx AxAy ,,il cetur*:: lEt r9\ 1 l6ElAF' J '

e x' + y3 + 3xy = I . find l|. '3[---

{,fr*Marks)\,frrgpp_-_

' .. .. '",CI2 0z iZ- 0zIf z: (x, y) and x=eo +e-u andy=e-'-e', provethat:--=* ;-Vfi.t0l Marks)

.) ^) D(u.v.w)If u = x+3y2 -23, y = 4x2yz, w = 222 -xy, find the value of

-

at (1, -1, 0)." A(x.Y-z),,,,':

',... ' (07 Marks)

Obtain ihe reduction formula for f sin" x dx . : (06 Marks)

A 1r- ? xdxE'v'aluate l----. (07 Marks)J lt )

i.!." -"Evaluate I If ., + eY )dydx (07 Mark$)

l3

lll

Evaluate [ |. [.''' ''dxdydz. (06 Marks)

J J J_000

t,Find the rurr. or l[f)r rrru rr,! vqru! vr

l(rL_

Prove that B(m,n) = g)]q.l(m + n)

7 a. Solve 9 -.'*-" +x' .e-" .

dx

b. Solve 4,Y =*' -y' which is homogeneous in x and y..'tr dx xy4a:^, dv V ,.:,,,.{., r c. Solve * -

,. ., = e'* (x + 1) .

'SL*

s ,s_.

$o*d* {< {< * * {' ..t' ' : / \t{u{\

(06 Marks)

.,.m,(07{arks)

-.%,*"

,,,':1''"r" (o6 Marks)

MATDIP3Ol

(07 Marks)

(07 Marks)

&L

j'hn ,*

.:: ::::::;, tuill'

==il;..=

..'1 '::: :a S

.=' * &d' lud

.:::''"':"

i ":1J' .' nl'S,::":l

:::,,,,":'13'

2 of2

USN IOME/AUITL33

Third Semester B.E. Degree Examinationo Dec.2013 lJan.2014Basic Thermodynamics

Time: 3 hrs. Max. Marks:100

b.

Note: Answer FIVE full questions, selectingut lesst TWO questionsfrom each pait.

PART _ ADistinguish between:i) Microscopic and macroscopic point of view.ii) Temperature and thermal equilibrium andiit) Intensive and extensive properties.Classify the following into open, closed and isolated system:i) Evaporator; ii) Thermoflask; iii) Passenger's train when stop at platform;iv) Refrigerant in a refrigerator; v) Pressure cooker; vi) I.C. engine duringcompression/expansion stroke; vii) Boiler and viii) Throttle valve. (08 Marks)

c. Define a Quasi-static process. A platinum wire is used as a resistance thermometer. The wireresistance was found to be lOohm and 16ohm at ice point and steam point respectively, and3Oohm at sulphur boiling point of 444.6"C. Find the resistance of the wire at 750'C, if theresistance varies with temperature by the relation. R: Ro (1 + oct + pt'). (06 Marks)

2 a. Does heat transfer inevitably causes a temperature rise? What is the other cause for rise intemperature? (02 Marks)

b. With a neat p-V diagram, derive an expression for workdone in each case of the following:i) Isochoric process.ii) Isobaric process.iii) Isothermal process andiv ) Polytropic process.

iJo()

o.

E

ooL

3e.

-loo,=co.= cn

Y{ro<-A

3*a::

o()

50i

-La6

3.J5i,iqo'!().-i

o:

!o5.Y>\ (Fboocb0o==<dgotr>o

lr<:-(J

oZ

oo.E

iii) the fraction of work done against the spring to compress it. (08 Marks)

3 a. For a non-flow system, show that the heat transferred is equal to the change in enthalpy of asystem. (04 Marks)

b. A gas undergoes a thermodynamic cycle consisting of the following processes: i) Process1-2: constant pressure P:1.4 bar, Vr:0.028m3, Wr2:10.5kJ; ii) Process 2-3:compression with pV: constant, U:: Uz and iii) Process 3-1: constant volume,Ur * U: : -26.4 kJ. There are no significance change in KE and PE. i) Calculate the network for the cycle; ii) Calculate the heat transfer for the process 1 - 2; ii) Show that

f Q = f W , and iv) Sketch the cycle on p-V diagram. (08 Marks)

c. A piston device contains 0.05m3 of a gas initially at 200kPa. At this state, a linear springhaving a spring constant of 150 kN/m is touching the piston but exerling no force on it. Nowheat is transferred to the gas. causing the piston to rise and to compress the spring until thevolume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25m2,determine: i) a final pressure inside the cylinder; ii) the total work done by the gas and

cycle cycle

c. In a certain stea{y flow process, 12 kg of fluid per minute enters at a pressure of 1.4bar,density 25 kglm3, velocity 120 ntls and internal energy 920 kJlkg. fne Rula properties atexit are 5.6bar, density 5 kg/m3, velocity 180 m/s, and internal energy 72OkJlkg. During theprocess, the fluid rejects 60 kJ/s of heat and rises through 60m. Determine work done during

(10 Marks)

the process in kW. (08 Marks)

lOME/AU/TL33

a. State the limitations of first law of thermodynamics. Illustrate with examples. (04 Marks)b. Prove that Kelvin-Plank and Clausius statements of second law of thermodynamics areequivalent. (06 Marks)c' A heat pump working on the Carnot cycle takes in heat trom a reservoir at 5oC and deliversheat to a reservoir at 60oC. The heat pump is driven by a reversible heat engine which takesin heat from a reservoir at 840'C and rejects heat to a reservoir at 60'C. The reversible heatengine also drives a machine that absorbs 30kW. If the heat pump extracts lTklls from the5oC reservoir, determine: i) the rate of heat supply fromthe 840"C source and iil the rateof heat rejection to the 60"C sink. (10 Marks)

PART - Ba. Prove that whenever a system executes a compete cyclic process, the quantit, {* =

,tort*ururrb. Explain principle of increase of entropy. (06 Marks)

c. In a shell and tube heat exchanger 45kg of water per minute is heated fi"om 30.C to g5oC byhot gases which enter the heat exchanger at 225"C.If the flow rate of gases is 90 kg/min,find the net change of entropy of the universe. (06 Marks)

a. Draw the phase equilibrium diagram for a pure substance on'I-S plot with relevant constantproperty lines. (05 Marks)b. What is the main objective of quality measurement? With a neat sketch, explain throttlingcalorimeter (07 Marks)c' What do you understand by degree of superheat? Steam initially at 1.5Mpa, 300.C expandsreversibly and adiabatically in a steam turbine to 40'C. Determine the ideal work output ofthe turbine per kg of steam. (08 Marks)

a. Derive Clausius Clayperon's equation for evaporation of liquid and explain the significance.

b. Distinguish betweEn: i) Ideal gas and real gas and ii.y Perfect.gas and semiper*.t|!'*X"*'(04 Marks)c. 0.5 kg of air is compressed reversibly and adiabatically from 80kPa,50oC to 0.4Mpa and is

then expanded at constant pressure and to the original volume. St<etctr tttese processes on thep-V and T-s planes. Compute the heat transfer and work transfer for the whoie path.

(10 Marks)

a. Explain the following:i) Generalizedcompressibilitychart.ii) Law of corresponding states andiii) compressibility factor. (06 Marks)b. Derive Vander Waal's constants in terms of critical properties. iot *".u.ic' Determine the pressure exerted by CO2 in a container of 1.5m3 capacity when it contains 5kgat 27oC. i) Using ideal gas equation and ii) Using Vander Waal's equation. (06 Marks)

) nf )

USN 10ME/AU32B

Third Semester B.E. Degree Examination, Dec.2013 lJan.2Dl4

Mechanical Measurements and Metrology

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting- -- --

-- - -__

^-J---- -'l---*---""'*-----'-'D

at least TWO questions from eoch part.

- PART_AI a. Define metre in terms of wavelength standards. List the advantages of wavelength standards

(06 Marks)

(08 Marks)

()ooLg

()6(.)!

8eylde;r,troo

.=N(o+

Eil.otrsaJ

3s6=

o()(o0

b0i

or=

=)Y^Xo.!o_a

oi;3aoE

LO

>'keo0

AEtr>:oVLo-

U<:'ooZ

Pa

over material standards.b. Describe with a neat sketch:

i) Imperial standard yardii) Wringing phenomena of slip gauges

c. Four length bars of basic length 100 mm are to be calibrated using a calibrated length bar of400 mm whose actu.al length is 399.9992 mm. It was also found that length of bars B, C andD in comparison to A are +0.0002 mm. +0.0004 mm and -0.0001 mm respectively and thelength of all the four bars put together in comparison to standard calibrated bar is +0.0003mm longer. Determine the actual dimensions of all the four end bars. (06 Marks)

(08 Marks)

(06 Marks)(08 Marks)(06 Marks)

(06 Marks)

(06 Marks)

2 a. Differentiate between:i) Hole basis and shaft basis system of tolerancesii) Interchangeability and selective assembly.

b. Write notes on:i) Compound tolerancesii) Gauge tolerance. 7 (04 Marks)

c. Determine the dimensions of hole and shaft for a fit 30H8li. ihe given data are:i:0.45Dr'+0.001D. IT8:25i.1T7:16i. Fundamentaldeviarion lorstratt't is-5.5D0ar.30 mm diameter lies in the diameter step of l8-30 mm. Sketch the f-rt and comment on thesame og Marks)

?. Explain with a neat sketch, the working of Solex pneumatic gauge. (08 Marks)b. Explain with a neat sketch, the construction and working of LVDT. (08 Marks)c. Show the arrangement of angle gauges, with a neat sketch by selecting minimum number of

gauges for the angles 32o15'33" and 54o36'42". (04 Marks)

1 a. What is the best size wire? Derive an expression for the same in terms of the pitch and angleof the thread.

b. Explain 3-wire method of measuring effective diameter of screw thread.c. Explain the principle of interferrometry. Write a note on optical flat.

PART _ B5 a. With a neat block diagram, explain the generalized measurement system with an example to

each stage. (08 Marks)b. Distinguish between: i) Primary and secondary transducers

ii) Active and passive transducersc. Define the following terms with reference to measurement system:

i) Calibrationiii) Hysterisis

ii) Sensitivityiv) Tkeshold value

a. With a neat sketch, explain the working principle of a CRO.b. State the advantages of electrical signal conditioning elements.c. Explain with a neat sketch, Ballast circuit diagram.

lOME/AU32B

(08 Marks)(06 Marks)(06 Marks)

""':"""

:'',,d, a. With a neat sketch, describe the Pirani gauge used for pressure measurement. los"tudrts)', ',,: b. With a neat sketch, explain the working principle of proving ring. (06 Marks)

*.-,,,.t*Olain with a suitable diagram, the working of hydraulic dynamometer. (06 Marks),:_,,,,.,,,,,,

8 a. Sk@,an0 explain the working principle of optical pyrometer. (0s Marks)b. Desciibe-=the steps to be taken for the preparation of specimen and mounting of strain

gauges. (06 Marks)

' ,,:,"";-.,,,: ,1,,, i.'l"t

,,,,%

' :"'.. t

,=:' ::: ::.."" -. ,,.

,:::, :::._ ,:.. .. 1

,::,:, :j:., a: 0".,,".i

:tI

I

'i ,;::: 1

:::::::: ',il$E

ir't;::" :' :"-"!,;.= -'",...,,,-"

iru 1r "j.:.. \-l

t"tttt'tttt"

:i,[ .;.

,,'',, ':t,, "

l,, ,..tt,,,,,,.'

'

't"""'ttt'i: ,r,1,' .

)jl( .

.1 :ia:, ,I

'il

2 of2

USN lOME/A.U35

Max. Marks:100

(10 Marks)0 Marks)

). \

.illi

{/\"/":- /

(08 Marks)

":" (12 Marks)

Third Semester B.E. Degree Examination, Dec.20L3 /Jan.2ol4Manufacturing Process - I

Time: 3 hrs.

2a.

3a.

b.

7a.b.

8a.

Note: Answer FIVEfull questions, selectingat least TWO questions from each part.

d)oo

a

o6)

3e

*oo I

Eoo.=NcO+

5*u(Jtr.Eo)

a:

oO

ooic!.69=26

-o(B3(]o.=

^Xtra-o.vo.a

o:6,iGH!o5.v>,hbo-cbo

tr>o-

U<-NooZ

Lo

la.b.

c.

b.

c.

PART - AList and briefly explain the different steps involved in a casting process. (08 Marks)Discuss in detail the different materials used in making a pattern. (06 Marks)Briefly dis,gqss the importance of binders and additives used in sand.moulding. (06 Marks)

List the types of moulding sand. Discuss the desirable prop :of moulding turd,o, Marks)

With neat sketch. explain jolt type moulding machine. (07 Marks)List casting defects. Discuss any two. (05 Marks)

With neat sketches, describe the,shell mouldingprocess. List advantages of the process.(10 Marks)

b. What is die-casting? With a neat, and lateled sketch, explain cold chamber diecastingprocess. (10 Marks)

4 a. With neat sketch, show the construcJion details of a Cupola furnace. Also indicate differentzones and write the reactions taking place in each of the zones.

b. With neat sketch. explain the working of a direct arc electric firrnace.

PART - B5 a. Explain the following, *ith neat sketches:

D Submerged arc welding. ,

iD Oxy-acegllene welding.and their fiekl of applications.

b. With neat sketch" explain forward and backward welding methods.

6 a. With neat sketches, explain the following:D Seam weldingii) Projectionwelding.With a sketch, explain the electron beam welding process and mention its applications,

(08 fuarks)

"111'lii

With neat sketch, explain heat affected zone (HAZ) and its various regions. (10 Maiks),;Explain the different welding defects, their causes and remedies. (10 Marks)

What is non-destructive testing? Explain with neat sketch ultrasonic inspection and itsapplication areas. (10 Marks)

b. With neat sketch, explain fluroscent particle inspection process and its application areas.(10 Marks)

USN

Time: 3 hrs.

Note: Answer FIVE full questions, selectingat least TWO questions from euch part.

PART * A

a. Define the following terms and mention their SI units:i) Capillarity.iil Dynamic viscosity.iii) Weight density.iv) Bulk modulus.

Derive Euler's equation of motion for an ideal gas.

State Bernoulli's theorem for steady flow of an incompressible fluid.

200 litres/s determine loss of head and direction of flow.

lOME/AU36B

Max. Marks:100

(06 Marks)

(08 Marks)(02 Marks)

Third Semester B.E. Degree Examination, Dec.2013 /Jan.2O14Fluid Mechanics

oo()

(.)

oL

3e(!=

7h;,=q

.=Nd+

9[ioi-O

o>a2

;!oO=l50tr-oE>d6-

'O cg

3o'XaOE

o-X

oid=6tE

L(j

5.e>\ (F^^occo

*oE>^Ov9a-

lr<*c.]o'7

oaE

b. Explain the effect of temperature variation on viscosity of liquids and gasses. (04 Marks)c. Two large plane surfaces are 2.4cm apart. The space between the surface is filled with

glycrene. What force is required to drag a very thin plate of surface area 0.5 square metersbetween the two large plane surfaces at a speed of 0.6 m/s, if the thin plate is at a distance of

(07 Marks)(03 Marks)

(08 Marks)

0.8cm from one of the plane surface? Take p : 8.1 t 10-rN-s/m2.d. Derive an expression for surlace tension of a soap bubbie.

a. Define the following:it Gauge pressure.

ii) Vaccum pressure.

il ;;:.;ri*il*;;b. A Caisson for closing the entrance to dry dock is of trapezoidal form 16m wide at the top

and 10m wide at the bottom and 6m deep. Find the total pressure and centre of pressure onthe Caisson if the water on the outside is just level with the top and dock is empty. (08 Marks)

c. What is a manometer? How they are classified? (04 Marks)

a. If for a two-dimensional potential flow, the velocity potential is given by 0 : x(2y - 1),determine the velocity at point P(4, 5). Determine also the value of stream function at thepoint P. (10 Marks)

b. Derive an expression for metacentric height of a floating body using analytical method.(10 Marks)

4a.b.c. A pipe line carrying oil of specific gravity 0.87, changes in diameter from 200mm diameter

at a position A to 500mm diameter at a position B which is 4 meters at a higher level if thepressures at A and B are 9.81 N/cm2 and 5.886 N/cm2 respectively and the discharge is

I of2

(10 Marks)

5a.

b.

IOMEiAU36B

PART - B

Derive an expression for the discharge over a triangular notch in terms of water over thecrest of the notch. (08 Marks)

A 30cm x 15cm venturimeter is provided in a vertical pipe line carrying oil of specificgravity 0.9, the flow being upwards. The difference in elevation of the throat section and

entrance section of the venturimeter is 30cm. The differential U-tube mercury manometershows a gauge deflection of 25cm. Calculate: i) The discharge of oil; ii) the pressure

difference between the entrance section and the throat section. Take coefficient of meter as

0.98 and specific gravity of mercury as 13.6. (09 Marks)c. What are the methods of dimensional analysis? Describe Buckingham's n-theorem for

dimensional analysis. (03 Marks)

a. Derive an expression for the loss of head due to sudden enlargement of a pipe. (10 Marks)

b. Determine the difference in the elevations between the water surfaces in the two tanks whichare connected by a horizontal pipe of diameter 300mm and length 400m. The rate of flowthrough the pipe is 300 litres/sec. Consider all losses and take f : 0.008. Also draw HGL and

(10 Marks)

(10 Marks)7a.b.

8a.

b.

TEL.

Derive an expression for Hagen Poiseullie formulae.An oil of viscosity 0.1 N-s/m2 and relative density 0.9 is flowing through a circular pipe ofdiameter 50mm and length 300m. The rate of flow of fluid through the pipe is 3.5 litres/sec.Find the pressure drop in a length of'300m and also the shear stress at the pipe wall.

: ' ; iv) Boundary layer ltlff::lDefine terms: i) Drag; ii) Lift; iii) Displacement thickness(10 Marks)

;:i.t:ffi:, e ror raminar boundary rayer nows given as +=r(*)-1rr;r.'.,",an expression for boundary layer thickness (61. Shea, stress (t6) interms of Reynold'snumber. (10 Marks)

2 of2