1OMAT31USN

Third Semester B.E. Degree Examination, June/July 201,4

Engineering Mathematics - lll,'{,. Time: 3 hrs. Max. Marks:10,0'" '_._

= ,,::i,

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

,,r*.S- "

yh";""= PART - A1*. ,::-e-Ci ,i -f.fl.[\ I- - f!. 1...()5 $; ^ g 1 'nzg I a.

*flde-forrier series of f(x) =2nx-x' in l0,2nl. Hence deduce f -+=4. Sketch

d/ _._.- ._ _ L_, ,r ? en_I\, g

I the graph of (x). ' (07 Marks)

E b. rina eoJ##i'*rir" series of f(x) =.*(ff)x, where m is positiv! ihteger. (06 Marks)E (r/.tj . \I/ :"';,,,ECB': c. Following table giygs current (A) over period (T):

utlon lor tlme J.) unl6. qtven

Revolution 5 l0 l5 20 25 30 35

Time t.2 1,6 t.9 2.1 2.4 2.6 aJ

b. Solve by graphical method,

Minimize Z= 20xr+10x, under the constraints 2x, *xr)0;x, +2*r<40 ; 3x, *x, )Q'4x, + 3x, > 60; X1, X2 ) Q. (06 Marks)

I of2

=lNEvulutlulllJlrwlrJlzwlzJlJwlJJlE Irime I t.z I t.0 | t.q lz.t lz.+ lz.0 | : I

g (07 Marks)

nAA $"* fvlacL,

*:1 lA(amp) | l.e8*H.30 I 1.05 | 1.30 l-0.88 l-0.25 lqdlPs I

E?B'+ Find (oT Marks).= C.l 1ov

E f r ,. ^"'"-e2x2 / - - \r r ,i -xl: --1r,---:-------rI ; Z a. Find Fourier transformation of"b*' j' (-- . I i *l hence show that "-%

i, self reciprocal.

E 'F \ *"" .* ,*, -* (07 Marks)

A Z b. Find Fourier cosine and sine transfoffiiiqr ofEE [x 0<x<?. ;

AE f(*)=il v\A\s (o6Marks)

Es' Lo x)a_L

Ee veintesraleouationo

: t'-s o<"s<' ,deduceit-cgsxo*=!.$E c. Solve integral equation [fqu;.orr*d* ={' .' " -' .-' . Herc(

IE ,4$:'' to sll 'o *' 2

€d

}A : , &u""h. Ozu ,Ozu.E ! 3 a. Find variour ffiibi; solution of one dimensional wave equdtioa

- = c' 1 :. by separable

3 f variable method. (07 Marks)(J-:

U E b. Obtain solution of heat equation "" -sr $ subject to condition u(0r't):0, u(.L t):0,d.= n c :":E!

I E *t{({Y0): f(x). .tr- (06 Marks)

$H C. ''Solve Laplace equation 3*3=0 subjectto condition u(0,y): u(,(, y) = u(x,0):0;E E ax- oy-

E g /-*\ i'

E 3 x, a) : ',,[TJ (07 Marks)

lr<o{ \'/.r cd 4 a. The revolution (r) and time (t) are related by quadratic polynomi al r = at2 + bt + c. Estimateo5 number revolution fot tr-gll ,14r,€1A

1OMAT31c. A company produces 3 items A, B, C. Each unit of A requires 8 minutes,4 minutes and2

minutes of producing time on machine Mr, Mz and M3 respectively. Similarly B requires 2,3, 0 and C requires 3, 0, I minutes of machine Mr, Mz and Ml. Profit per unit of A, B and Care Rs.20, Rs.6 and Rs.S respectively. For maximum profit, how many number of productsA, B and C are to be produced? Find maximum profit. Given machine Mr, Mz, M: are

available for 250, 100 and 60 minutes per day.

PART _. BBy relaxation method, solve - x+6y +272 = 85, 54x +y +z = 110,

(07 Marks)

:}it.:},*.,*r*,1,! 2x+l5y + 62...=72.y + 67..,-72.

60?$aarkg.geclpiocal of

6a.

b.

r''l * fl=%.,.* Using Newton Raphson method derive the iteration formula to find the value ofreci

1w.J@:: I *#q't{ popitive number. Hence use to find :- "r"r;w.. e

upto 4 decimals.#"k t".\*3 (06 Marks)

h,.

rayley method find numerical largest eigen value and, .orresponding eigen'. li'.2 l1 - ^,r . *,',J\: .

lution is form€4b; rotatfnqfudbout x-axis, the area becurve throush the.ffiihts wfthrthe followins co-ordinates.x 0 U6 2lS'=. 3/6 4t6 516

v 0.1 0.8982 9.9CI1€ 0.9589 0.9432 0.9001 0.841s

3/8* rule, find vcrfuiu$of solby Simpson's 3/8* rule, find vofufoSof solid feqned. (07 Marks)

,.,.={;.}' 0r-1!-+!-1fl---ro '' ,,..

State and prove recurrence relation of f-tansformation hence find Zr(n), Zr(n').Find Zr[e'e coshn0 - sin(nA + 0) + n].

Solve difference equation un*z * 6un*, +9rn = n2' given uo = ur - 0.*t*rt rl.

2 of?

u*[ro2tl --.'\vector for

{

-?

.,,r0 i I uring (l , 1, 0)r as initial vector. Carry outfrd,.?teflations. (07 Marks)

l, ,n lo.ld ...-- ::. ':: ::'

Fit interpolatingffinomial for f(x) using divided diffe$qp"formula and hence evaluatef(z), given (0)::'B' )

: -14,f(4): -125, (8) : -21, ffi: lSS. (07 Marks)Estimate t when f(t) ryffi,qsing inverse interpolation&rmirla given : (06 Marks)

c. A solid of revoX:0, x: 1 and

tween x-axis, lines

-'1". - O2u aua. Using the Schmidt tw,S&vel point formula"psolve *=lunder the conditions-a-,,,= P ,I Ax' A

llu(0,t):u(l,t):0gae,b0; u(1,0):sin nx 0<x< l,iakeh: i a: ).Carry out3 steps

,," {,,q*/ ,::.'.'--.'.,''-....... 4 6ln tlme level. , - (07 Marks)

, "..rf ':'' ,::11"1

b. Solve tlr.r.#dfb equation *=a{subject to u(0, t): u(4, t): ur(xo 0) :0, u(x, 0): x(4-x)A+' tu-vl uL

take-h*,I n^,Ot $r (06Marks)

. 6b#;e *! -0 in the square mesh. carryout 2 iterations. ** , (07 Marks)dx' dy'

.,,r...,1...

,..'.:- "

'oool-&l---!+4--l'ooo

8a.b.

c.

(07 Marks)

(06 Marks)

(07 Marks)

USN MATDIP3Ol

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

Third Semester B.E. Degree Examination, June/July 2Ol4Advanced Mathematics - I

,,,'.Time:3hrs.I ai+:'

_1

....,r ...';.

f i ..a* Find the modulus and amplitude of

Note: Answer any FIWfull questions

= 2l*'ro.'n4

5,. ,",,,,t,,,,,

'';;

,;:.,lft'

il)ooCdLo.(n

qd

ocnc)!

EqX=J'd95r'oo ll

troo.E i.ic6+!r ooYo()qdO

Eseso-*oQ

o!b0cdctE!BEditd-bB'5s

d. 8_tro.6(noj

9Eto@tEaE9O

3E>tbo-tro06)=

=d!i96sa-.

o {,; e.i

Ooz(sL

o.

b. Prove@_, (1 + i)' + (1- i)" !)'ql$i. =

'u'%,,...':',:l -

c.

2a.b.

c. Ify:acos(logx) +b sin(logx), t{gnpgovetiiat x2yn*2+(2n+ l)xyo+r +(n2 + 1)y":0

,,ffi (oT Marks)

a. Find the angle of intersection o$tp'€Urves f :sin 0 * cos 0, r : 2 sin 0. (06 Marks)

b. Find the pedal equation of thd'ou*e rn: an cds rS. " (07 Marks)

c. Using Maclaurin's series expand log(l + sin x) upto the term containing xa. (07 Marks)

z z '".""",. :!* ( a- o- \ 2 / o- a- \

/.t r\ A ^b. If u = r;rr-'[

i' + y' '1, th., prove that x$+ y+ = tanu (06 Marks)

\ x+y ) ax 'Ay

.""J t; +3f -:z3,v:4r,'y, w:222-Xy,evaluate ffi at(1,-r,*r.* llrMarks)

r I 2 4qrtj

t" = Ith n x dx (06 M .r

0 ";:,.,'1,,,,,,':'

r 4sin 0

b. Evaluate J J r'drde (07 Marks)0 2sin0

lz x+z

c. Evaluate II J(. +y+z)dxdydz (07Marks)

-l 0 x-z

L of2

6 a. With usual notations, prove that

MATDIP3Ol

(06 Marks)

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

,4*. F(m,n) - {T) r(n)

'E- .,:*n'n,, dA-Sfu

Show that J.Gio e ae, [ + = "{3* o dr/sinO

c. 'Pi6y+that }Gn,Yr)- 22^- t B(*, -)-{ :

"*ffi-a. sorve jl;g:+ y+ r)', iry(o) : 1.

'./ *b. Solve tx + r).S4,+ e,. (x + 1),

ox

"{l*-,1t,. =

)$- ''*,,,,4$'

-' a1,.= 4

ii" 1rs#;

'i,dld'.:ll!'

2 of2

USN IOME/AUITL33

Third Semester B.E. Degree Examination, June/July 2014Basic Thermodynamics

-d-,.Ti*e: 3 hrs. Max. Marks:lffi+i".3 Note: 7. Answer FIVEfall questions, selecting ry"Fffr,* -.l;rff!,.: at least TWO quesfionsfrom each part. ,:,.,- 1

= =";: 2. Use of thermodynamic data handbook and stesm tables is pqgnitted.."-"4)t€ u,."..:......,. .'H ,,,.,,,,i'..- PART - A€' I a. Deftp the following :d.: (r) ruigh system (ii) Closed system and (iii) Isolated systdu , and classify thes^::n foilowih$,iato open closed and isolated system and explain giving",+eh'sons:

d E (i) Radiatii car (ii) Thermos flask (iii) water pump tf ;n rsure cookeloz

rvr"rx.)

8.E b. What are internaffiffil fixed reference points? Name few of &tm. What is their importance?-v5Ee a r (05Marks)

=? e*k ^ rr\E.ll c. Define a new temperaffi4cale 'N' in which

troP r e" ro:E $ 100 'N and 300 oN respdbfuely. Correlate thiE i., IUU "N and 30U "N respett&ely. Uo6$

E a" which freezing and boiling poffireo F "1*

o-

){S f 'v' is specific volume in (m3/kg). For this fluid find c, and cy (ie., specific heat at constant

: fr pressure and specific heat at constant volume). If a system composed of 2 kg of this flufd,ir.v

ij expands in a frictionless piston and cylinder machine from an initial state of 1 MPa, 100"C

2 to a final temperature of 30oC. If there is no heat transfer, find the net work for the process.

E (08 Marks)E

3 c. A blower handles 1 kg/s of air at temperature of 20oC and consumes a power of 15 kW. The: inlet and outlet velocities of air are 100 m/sec and 150 m/sec respectively. Find the exit

temperature of air, assuming adiabatic conditions. Take cr: 1.005 kJ/kg K.

EE **,ioE E 2 a. Starting from a convenient commbn*stqto pdint, on P-V diagram, show the four expansionvF

E f processesforn:0,fl:1, fl:y$qlekegisspecificheatratio)andn:co,whatareeach.-U

; E processes called? Indicate their a@g$ Sttjac,ent to the processes on the diagram.

-!\

SET I c. To a closed system 150-kJ#work is done on it.tf.ttre;tlitial volume is 0.6 m3 and pressure

E E of system uuries as follpws: fr*€ * p: (g -.4y), d)-2. ts

E ; where 'P' is p,hiqs3?e in bar and 'V' is volume in m3.%dg&mine the final volume and

FF ' ;r"."; E 3 a. Write tlqe.steady flow energy equation for an open system and exp@p,'the terms involved inE E it. aMffimpht/ SFEE for the following systems: * ,ti,,.

F; idffi;";tr"."ilJ^6il;;i; H ,r (o6Marks)!oA E b.. -The properties of a certain fluid are related as follows: . P' .^X fur

E € ,,,-.*., Pv : 0.287 (t + 273),S Io ,,- .='"" u:0.718t + 196 *,{ ,

EE ' 'tJt)E d .. where 'u' is specific internal energy (kJ/kg), 't' is temp h oC, 'P' is pressure in (kN/nf) and

L of2

(06 Marks)

IOME/AUITL33

4 a. State and prove Camot's theorem. (10 Marks)

b. A heat engine is used to drive aheat pump. The heat transfer from the engine and heat pump

H * are used to heat water circulating through the radiators of a building. The efficiency o*Q*" .&;. heat engine is 27 percent and coefficient of performance of heat pump is 4. Evaluq$ro-ft=

% _ ratio of the heat transfer to the radiator circulating water to the heat transfer ro,n

iffiu,'' .:'"', PART - B i.,.

't.,1,;iq,

5 a. St;Gl rove Clausius inequality? What is the significance of CU;ipriribeuality?o Marks)

steel oI LU Kgwz /-u ls rmmerseo m oll. ueteflmne cnang€ m'pmropy Ior tne unlverse.Take specific heqt pf oil: 3.5 kJikg K; Specific heat of sQefrpall:0.5 kykg K. (10 Marks)

1+* W.\-6 a. Define dryness fracti&*6- team? What are methods::usedlo measure dryness fraction? Withneat sketch explain anfMFmethod. !*;'

(10 Marks)

*",tt .. F.- ir * (10 Marks)

b. An adiabh@ffisel contains 85 kg of oil at a temperature of 21"flS4 spherical ball made ofsteel of 10 kdry$@27"C is immersed in oil. Determine change 1fohltrronV for the universe.

""*::-"**b. A rigid vessel of 2 nt' volu,i ,p is filled with superheated steam at 20 Bar and 350"C.The vessel is cooled until the steagq jus{@*aturated. Calculate the mass of steam in thevessel; the final pressure of st@ifufqnfl'Yinount of energy transferred as heat to thesurroundings. (10 Marks)

(04 Marks)

undergoes a polytropic change

(06 Marks)

to a pressure of 15

on or by the airit is an increase or

(10 Marks)

d.

7a.b.

| \\. __ , \_2,/ r'1.- i. :: '"ll

0.2 kg of air."wltlhpressure 1.5 bar and temperattxe 27"C is6c. u.l Kg oI orqwl{H-pressure l.) bar ano temperature z/"u ls (

bar acco.r4ry!}to the law PVr2s : constant. Determine (i)rqwl{H-pressure l.) Dar ano temperature z/"u ls

ry!}to the law PVr2s : constant. Determine (i(ir)

trlr(, (r/ wto or from the air (iii) Change of entropy stating

entropy. For air R: 0.287 kJ/kg K r: l.4,Cy:0.718d*-\&#"

8 a. ".$ffte notes on the following :

. {1ii) Dalton's law of partial pressures,,, =' '' (it) Vander Waal's equation of states

.",,*l',ft (iii) Generalizedcompressibilitychart

. ,u;,*if b. Determine the pressure exerted by carbon dioxide in a container of 1.5!{la;. contains 5 kg at27oC byusing- (i) Ideal gas equation (ii) Vander Waal's equation

Take the Vander Waal's constant a: 365.6 kN-ma / (kgmol)2 ;b: 0.0428 m3/kgmol

Universal gas const: R- : 8.3144kJlkgmol K.

{.**r(*2 of2

!l .

, .. .::.

(1f IVSArks)

m3 capacity whcfr:ii.,,

, ,.*t: *" '"_

Write Maxwell relations and exfujftdthe terhu igvolved.i,,,. Afl { -d

Show that the change in pqmopy when a ffiTeqt gas

PV': Constant is given -h$-lhe expression {

(08 Marks)

IOME/AUIPNIITL34l

USN

Third Semester B.E. Degree Examination, June/July 2Ol4Mechanics of Materials

'u*,-,,,, ''*"' 3 hrs'

' !t' l' :.'i*il',1lrrr '!

.r

::. .::.

Max. Marks: lpugl,,,

Note: 7. Answer FIVEfull questions, selecting 'at least TWO questions fro* each parl

2. Missing data may be suitably assumed.C)o(.)C6Eo.d

(n

()dC)!

ER(n=;;69=r)oo ll

<oo.E a.rd$HOOx0JotrFO

Esa=

iio-9doOEboc.9dP6

.od

']?o!o

?o90-tro-6doj

9EgoalE

!o'< .!l>\ (*.oootr ol)

o5P.9Fbio--: Pr

^q\J<-.; el

o

z',oo.

t, .,,, ,,,'l I PART-AI a. ftfi!€ (i) Stress (ii) Hook's law (iii) Elasticity (iv) Lateral strain. ,,," ,,t,," (04 Marks)

b. f*llaia^stress-strain relationship showing salient point's on the diagrarn "' ' (06 Marks)

c. A stepp'd."bar_ is subjected tg .an gxtelng] 9$ile as shown in=@

change in

?oAlnil-60il

Fig.Ql(c) . Fig.Q3(c)2 a. Define (i) Poisson's ratio fiilBnk moduHis-$ . (02 Marks)

b. Derive an expression for dsttfblishing the rellstt-aship between Young's modulus andmodulus of rigidity. (06 Marks)

c. A 25 mm diameter std iod passes concentrically fu gh a bronze tube 400 mm long,50 mm external diaptp&r and 40 mm internal diameter. T}y6.qnd of the steel rod are threadedand provided withx-*uis and washers which are adjusted fuiftial-ly so that there is no end playat 20"C. Asurriffig that there is no change in the thickness 'bfJk,washers, find the stressproduced inihe steel and bronze when one of the nuts is tightenedffigiving it one-tenth of aturn, the,brltin of the thread being 2.5 mm. Take E for steel : 2-Q0 =kN/mm2

and E forbroqza,,; 100 kN/mm2 . ,,""''.=-,,, (12 Marks),. '=

3 a. ..,,,1 fine the principal planes and principal stresses. (04 Marks),b-:l=Explain procedure for constructing Mohr's circle, for an element acted uponW,t tensile

,, ,,,, " """ stresses and shear stresses. (96 Ularko

", , ', c. The state of stress in two dimensionally stressed body is as shown in Fig.Q3(c). DEbr, rnrthe principal planes, principal stresses, maximum shear stress and their planes. (10 Marks)

twAln/ lw illwu>

6oillwnL8o NluuL

4 a. Define (i) Strain energy (ii) Work. (03 Marks)

b. Prove that volumetric strain in thin cylinder is given UV # tS - ap), with usual notations.1LL

(07 Marks)c. A C.I. pipe has 200 mm internal diameter and 50 mm metal thickness and carries water

under a pressure of 5 N/mm2. Calculate the maximum and minimum intensities ofcircumferential stress and sketch the distribution of circumferential stress and radial pressureacross the section.

I of2(10 Marks)

5a.b.c.

6{

'"/':i' "'

IOME/AUIPM,ITL34

PART _ BDerive the relationship between load, shear force and bending moment. (05 Marks)Briefly explain the different types of loads. (03 Marks)

Draw SFD and BMD for the loading pattern on the beam in Fig.Q5(c). Indicate the point ofcontraflexure. Also locate the maximum BM with its magnitude. (r2 Mqr_lt$ "

. ^r I -,r.r

6a.b.

c.

'"'.,,,,-"..--;.:.., Fig.es(c) ,, ''

,'1'

,,o-

Whatqde:the assumptions made in theory ofbending? (04 Marks)

Prove thdpk maximum shear stress is 1.5 times the average ai stress in a beam ofrectangular*efoss;section. r,,, (06Marks)

At a given poifiion_in a beam of uniform I-section is subfebted to a bending moment of100 kN-m. Plot the variation of bending *t:t:Ty.s the sec&ion. [Refer Fig.Q6(c)]

I l6D rntn - t

$T#T-1,,L ,$

$'J-L1Fig.Q6(c| (to Marks)

7 a. Derive the deflection, equation for the beam in the sta l form1.r

er$i*nar*1. (06 Marks)dx'

b. For the beq4p;,loaded as shown in Fig.Q7(b), find the position*ffi.Hrmagnitude of maximumdeflectio-kl$dff<e I:4.3x108 and E :200 kN/mm2. (14 Marks)

"r ll..lq, qotl!, | ,, n

]:::: ::::

Lat are the assumptions made in theory of columns? 103 Markg'8 a. What are the assumptions made in theory of columns? t'in' b. Derive an expression for the critical load in a column subjected to compressive load, whgflone end is fixed and other end is free. (07 Marks)Find the diameter of the shaft required to transmit 60 kW at 150 rpm if the maximum torqueis 25o/o more than the mean torque for a maximum shear stress of 60 MPa. Find also theangle of twist in a length of 4m. Take G: 80 GPa. (10 MarHs)

*(*{<**

2 of2

l J 4o -1, sv)

Fie.Q7(b)

USN IOME/AU32B

Third Semester B.E. Degree Examination, June/July 2014

* Mechanical Measurements and Metrology tu-^ ?q,,W=

%'*'*Ti&e: 3 hrs. Max. Ma&:1b0

n.,," -" :.

u ,,llli.": Note: Answer any FIVEfull questions, selecting ,'$d:.1

€ ''""'.,"";,,r+.*. atleast TWO questionsfrom each part. . . ' "...nEo, .' 'ir+

EdF:::

H "--,. PART-A {-'_',t 16 ro 1'€ ,ro\ lf'g I a. Sketch and expl5ip.the following:

=.u'r&x

o ,^ idi- A -

. E I a. Sketch and explaip.the following: . #*'n()8o5 i) Impherial st@rd. j* \6-

-?E ii) International pbtotype. --l (08 Marks)

E a b. Discuss the following st@rds of measurements *ltfi tt "ir

characteristics:*r,g, * i) Line standard.

cB$F * c. What are the major requirementsrofe{ip gauges? (04 Marks)YiDJ

ll&Ipe roilowlnsWrd.mlffip*type.rwing Sffiardsard. '".,,,,',,,:,,,,,,,,

l^-l ::,..7 ,t

vith sketch:

t u*M1fiA D Nominalsize. -, f-q;f 'aRr

; E ii) Basic size. '*;f ts 6-I f iii) Actual size. .i q*" '"'

,^ ..E i iv) Zero line. { "8.E v) Allowance.(Bci

t ; vi) Fit. (oe Marks)

E E b. Differentiate betweon hole basis and shalt basis system with sketches. (07 Marks)

; E c. How the plain gauges are classified? (04 Marks)Ei

t e a

9= *" -u

} S 3 a. List the &apCteristics of a comparator. " 'i . (06 Marks)

E € c. Giv}'"Ylie combination of angle gauges to obtain the following anbffi also sketch the

A € arrangement of gauges: i) 37" 9' 18" ; ii) 33' 16' 42". :" (08 Marks)d.!

=uLO

9, i 4 a. Describe with sketch 3-wire method of measuring effective diameter of the thread" (t0 Marks)

ry i, . b. Explain with sketch measurement of tooth thickness of a spur gear using gear tooth Vernier.E q r ---- - ---r--- o---- -----o o---- ---

* t Caliper. (t0Mark*)F-0)F>

3g= ) PART_Bot-: c.i

i, 5 a. What is measurement? Explain the fundamental methods of measurement. (06 Marks)

2 b. Explain:

E i) Repeatability.

X ii) Sensitivity.

"E iiD Hysteresis. (06 Marks)c. With suitable example, explain the stages of generalized measurement system (08 Marks)

I of2

F'I

i,a:

lOME/AU32B

6 a. Explain with block diagram working of a general purpose oscilloscope. (10 Marks)b. Explain with sketch:

i) Stylus type oscillograph.

.::.. ii) Light beam oscillograph. (10 Marh):i' : :-

"''iff=.,i u. Describe with a neat sketch the working and applications of a proving ring. tffffi"fiO"*'-.,44h: With a neat sketch, explain the working of a hydraulic dynamometer for the meaffient of

*.i="'Jorque. dft -'1S7 Marks)

cfufullain the Bridgemen gauge with a neat sketch. $ ',;*: (oz Marks)- *\J* *.3,

8 a. Wiitga note on thermocouple materials. i, '- (03 Marks)b. With rypftat sketch, explain the working of a optical pyrometer. gu tu& (08 Marks)c. Show vifr4}#s*ctr how the strain gauges are mounted to measure,idtbe*following cases:

i) Axia@in only. ,*f #"'il, i:l$:Hfl'd&# #ffi' (oeMarks)

fuk"*N* /q"-die- $.'vd's *dlsu \o, l: d\L*l\ *****{#"e\'"tftw ,* fl...*

{,i,qt*q}d{r\ s \_j

l-\/ 'Ed--

=;*,,,Y ffi*^*_ q.

*\-", ;

2 of2

USN lOME/AU36B

(08 Marks)

Third Semester B.E. Degree Examination, June/July 2014Fluid Mechanics

,,,,, Time: 3 hrs. Max. Marks:l@,,,'.' Note: Answer any FIWfull questions, selecting it

"

:'i: ', . atleast TWO questions from each part.

1

PART - AI a. rr*@i,ye reasons: , .:::

i)1,1-) p, *umic viscosity of gases varies with temperature. ,_ii) ',i@vitation must be avoided in most of the flow systems. j u". (04lVlarks)

b. Derivdfl#relation for pressure intensity and the surface tension, inq's€-of soaf bu!i$'--'r'li,;,r. ,*,lr* " (04 Marks)

c. Determine tfie"dpqsity and mass of air in a room whose dimQruitins are 4m x 5m x 6m at

d. The viscosity of the fluid is to be measured by a viscome$& constructed of two 75cm long

0)oc)dLa(o

q(n

-t o:OL

E9d=dj-

-:r F69

=r)-oo ll

<oo.= ..1d$

bx0oq-O

EsaX

b6cdO

boc

-Gd-

5()5 .!J

a. 6_tro.oia.YOEtc)a l.E

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concentric cylinders. ffie.outer diameter of the inne{*yJinder is 15cm, and the gap betweenthe two cylinders is th&'The inner cylinder is Ybtated at 300rpm, and the torque is

measured to be 0.8 N-m. Deterrn-irre the viscos{t{fiithe fluid. (08 Marks)

2 a. Differentiate between absolute,ffigr-4nd;;il pressures. Represent these pressures on achart. *l}fl}e - (04 Marks)

b. Derive the expression for total pr_e5S 1,Stce and depth of centre of pressure for a verticalplane surface submerged in liquid.r'r;i"'' '111-+

\ (10 Marks)

c. A differential manometer is c"gane'dted at the Ftrp points A and B of two pipes as shown inthe Fig.Q.2(c). The pipe A contains a liquid of sp*ugravity : 1.t while pipe B contains a

liquid of sp. gravity :,.,p .'tthe p.ess,ries at AilHfrd B are 9.81N/cm2 and 17.66N/cm2

,,;5 a. Differentiate between:i) Steady and uniform flow.ir) Laminar and turbulent flow.iii) Compressible and incompressible flow.iv) Centre of buoyancy and centre of gravity.

=,,,CI;9."The pressures at 4fu#fid B are 9.81N/cmz and 17.66N/cm2

d$ference in mercury level ih t&,xdifferential manometer. Take sp.

t.6. (06 Marks)

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b. A wooden block of size 6m x 5m x 3m height floats in fresh water. Find the depth ofimmersion and the distance between centre of Buoyancy and centre of gravity (BG). Sp.

gravity of wood is 0.7. (04 Marks)

c. An idealized flow is given by V : 2x3i - 3*'yj. Is the flow steady or unsteady? Determinethe resultant acceleration of the fluid particle at point P(x, y, z) : (2, 1,3).

I of2

(08 Marks)

lOME/AU36B

a. State and derive Bernoulli's equation for fluid flow. State the limitations on the use ofBemoulli's theorem. (12 Marks)

b. Water is flowing through a pipe having diameters 30cm and 15cm at the bottom and upper

..t end respectively. The intensity of pressure. at the bottom end is 29.43 N/cm2 and the prels:Pre,4*- at the upper end is 14.715 N/cm'. Determine the difference in datum head if the rate of flow

5 a. U_$ketch and derive the relation for actual discharge through a venturimeter. - (08 Marks)

b. Find.the discharge over a triangular notch of angle 60o when the head oveh the triangularnot&,b P*2-. Take Ca:O 6. . y:.* (04 Marks)

c. The vffi]es controlling the motion of a floating vessel through ymfQfi.are the drag force F,

the speed'ffidre length L, the density 6, the dynamic viscosity I of water and acceleration

due to grurQ".,$.,Dirive ur, .*pr.rr1on for F by dime*lgryJfe?frlysis. Use Buckingham

#6 a. Derive the Darcy-W-iffih equation for the loss of hecd due to friction in a pipe. (10 Marks)

b. Sketch the TEL and HGfu'fer.a pipeline connecting twb reservoirs. (04 Marks)c. A 5cm diameter pipe takes&{ from a large fiank and runs Srn, then suddenly expands to

of 1.5 m/s. Compute the nec ighl8f'water surface in the tank above the point ofdischarge. Consider all the minor ake f : 0.0065 in the Darcy equation. (06 Marks)

7 a. What do you mean by viscous fldp?}d * , (02 Marks)

b. Prove that, in a laminar flow thro;ugfi pipe, ,6tp$V distribution across the section of the pipeis parabolic. Also sketch ,ll@,Yelocity distriBtftiUl'l and shear stress distribution across a

section ofpipe. o*" (10 Marks)section ot'ptpe. "ff;:- n. t (10 Marks)

c. Determine: i) The pr-eq$e gradient; ii) The shear s'trep$at the two horizontal parallel platesand iii) Discharge..6-ffieter width for the laminar floW df oil with a maximum velocity of2mls between trgih$ruontalparallel fixed plate which are,t00nom apart. Given, V:2.4525),

- "\{*tr :8 a. ExperipqQ.iftS were conducted in a wind tunnel with a wind speed df,8"qkn/hr on a flat plate

of si@n long and lm wide. The density of air is 1.15 kg/m3. The t@icients of lift anddgagi.are 0.75 and 0.15 respectively. Determine: i) the lift force; ii) gr. drag force;

r-@)'th" resultant force; iv) the direction of resultant force; v) power exertedby air on the

ryf1hte. " ""'{'ri(lo Marks)

"..r&g: Differentiate between : i) Sonic flow, subsonic flow, supersonic flow; ii) Ma0h,number,

;ilt' I' mach angle mach cone. (06.t$arks)

.:,{hl c. Determine the mach number and mach angle, if a projectile travels in air of pressureoqd''"" 10.1043 N/cm2 at 10oC at a speed of 1500 kn/hr. Take K: 1.4 and R:287 J/kg K.

,,,, '

(04 Marks)

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2 of2

USN lOME/AU35

Third Semester B.E. Degree Examination, June/July 2Ol4Manufacturing Process - I

. Time: 3 hrs. Max. Marks:l00

o i'-1',., at least TWO questions from each part. . .

,,,1* PART _ Aii ""::I a. " w'ith a neat flow diagram, explain the steps in olved in metal casting procsq. Also write thee

' attrvatrtages and limitations and applications of metal casting process. ,'-,, * .1'" (12 Marks)

b. WhaL arq.,.pattern allowances? Classify and write a note on draft allowance and distortion

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allowa h figures. ,*_,,,,,=,,.,,"""' (08 Marks)''''{""11

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2 a. Name the ba-sb"sads used in metal casting and briefly discuss-futequirement of base sand.

b.

3 a. Briefly explain the characi.iisti. features of FTIRAN and ALKYDE type no bake mouldingprocesses. '-,., ,: " (10 Marks)

b. Name the centrifugal casting nf6$oqrs. With-neat sketches explain the working of verticaland horizontal type true centrifugal'{mfug-'processes. (10 Marks)

.,{ H?"'.4 a. With a neat sketch explain the wofk'l1@ p?inCiple of coreless induction furnace. (10 Marks)b. With a neat sketch explain the 1yoffing principp.pf 3-phase electric arc furnace. (10 Marks)

PART _ Bp,,f,"t'"t,' rl\l1l - -ED ::r-

5 a. With a neat sketch ex@ift the principle of Laser wel{iqg process. Mention its advantages,limitations and applications. (10 Marks)

b. With a neat sketch explain the thermit welding procesd:. -Write the advantages andlimitations.

.. _ -'ffi,,r, (ro Marks)

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6 a. With a qgfiit sketch explain the working principle of oxy-acetylene.gas=welding. Also writethe f.h"&libharacteristics. (12 Marks)

b. Erytraln Tungsten inert gas arc welding process with figure. Mention its adv4ntages.:''",,,""' (08 Marks)

, .,' ',,,r,,,,,,.....,:ii: . '

7 Write short_notes on the following :

0,"i" b. Shrinkage and residual stresses in welding s "

"",,' "" c. Welding defects and remedies ,,..,.. ,..,d. Electrodes (20 Marki)

8 a. Distinguish between soldering and brazing. Also discuss briefly the furnace brazng processwith figure.

b. With neat sketches, explain thecasting and welding:(r) Eddy current testing

following types of non-destructive method, "f

irrl::ffiT)r

(ii) Acoustic emission monitoring.

:f***,f

(10 Marks)