.', l-13-DT:--.-'.t.--

C,:,n, -EJ5-13

(c)

{d)

ta)(b)

,3t rnl rr\(ctrill

AI4 _E

(3 Hours)

(S2 +45+13)2

6

6

TURN OVER

5-€l tt

\B i (1) Question No. 1 is Compulsory.(2) Answer ary Three from remaining.(3) Figures to the right indicate marks.

F rnd laplace of sin{ 5

)ho*'thatthe set of functions slnf$ ) -' /3rx\ ^' /5rx\\"C )

t'' [zf-i' t't [1t-J is orthogonal over s

iO. L).!}isr\r thatu:sinxcoshy +2 cos x sin hy +, 2-tz + 4xySatisfies laplaceequation 5

:ni find iis corresponding analytic function f(z): u i-iv.D:;ermine constants a,b,c,d if f(z) : x2+zaxy1br' * i(cx2+2dxy+y2) is analytic. 5

. .:c complex forrn of fourier series f(x) : e3* in 0<x<3 . 6

'--. ire Crank Nicholson Method solve ut : u** subject to u(x,0) : 0 u(0, t)=0 and 6

1. (a)

(b)

ufl,t): t for two tirne steps.

i c) Solve using laplace transform , *r y : t, y(0) : l, yr(0) : 0dt"

{,a,I Fi:nd bilinear transformation that maps the points 0,1- oo of the z plane into -5, - 1,

3 ofwplane. I

By using Convolution Theorem find inverse laplace transform of

Find fourier series of f(x) : x2 -TE 5 x S n and prove that

(i) +=? i,? p (-l)'* l

iu) E=i -7-n:2 lll(iii) -T= ?*?*?*..-

*-t-16rta'Eluate J "

0

sohe * -r,aE'

6

6

I

xhz, o*t

9:ou,ct

t'-lL,/

C

I I-r i-[3-.]Tyrtrl-25

Con. 7&15-GX -12025'13.

Bender sshmidt method subject to cooditions u(o, t) : 0 u (x, 0) : 0

u(1, t) : t taking h : 0-25 0 <r < 1

2z-3(c) Ob(aio r*'o distinct Laurent's Series for f(z) : 7f;; in Powers of (z'4)

indicating Rcgion of Convergence'

r(.ai Eralume J Z'Ualong

0

(i) line y: x(ii) Parab olax:Y2Is tine independent ofpath? Explian'

tb) Find half range Cosine Series for f(x): ex

(c) Find analYtic functionf(z): u * iv such that

Cosx +Sinx -e-Yu-v: --T--y-2Cosx -e *e

0<x<1. 6

8

rvhen rff)=a

6" (a) A tiglrtly streched sting with fixed end points x : 0 and *: t lthe shape defined

byy:I(x 0- x) whereKis aConstant is released fromthispositionofrestFindy(x,t)

The vertical disPlacement

02 y ^, O'yif ;f =c'a?

(b) Find image of region bounded by x = 0, X= 2y:0 y:2 in the z plane under the

21t do(c) Evatuate l;;m

I

6

6

rLr-]i-- ,/

8

t

/-.i

9.b ,Lf"uir-l r-r l-r3-DTP:8-\L-::

Con. 7883-13"

{tu"fi *,*TD

E/V $-'13

b,h:2lftrlr(3 Hours)

GX-12068

[Total Marks : 80

\.ts, : 1r Question\o. l is compulsory.

i r .\ttempt an1' three questions out of remaining five questions.

I t Use of steam tabels is permitted.

:';:.'r:r anl.four of the following :-

, State and explain Maxwell relations.

: , Claussius inequality.

. , -:,drabatic flame temperature.

: Second lar.v of thermodynamics.

a,-.ru1e'sexperiment.

- Second lalv efficiency.

, S: r\r ihat the conversion of work into heat is complete and contineous. 4

: S...:t tlo*'s into aturbine, at a flow rate of 5000 kg/hr" The turbine develops a 12

: . '... -: ri 5 5 0 KW The heat loss from the casing of the turbine and the bearings is

._:=-----'lg.

. F:nd the change in enthalpy across the turbine, if the inlet velocity is negligible

;nd erit velocity is 360 m/s and the change in potential energy is negligible.

. . F ind the change in enthalpy across the turbine, if the velocity at entry is 66

m s and the inlet pipe is 3 m above the exit pipe.

- S:.:'i'. :hat entropy is aproperty of system. 4

Heat florvs through a wall at a rate of 3 x 105 KJ/hr. The temperatures of two faces

ofthe rvall are 321"C and207oC. If the surroundings are at27"C, What is the loss

in available energy?

State and prove carnot theorm.

:. .::iot heat engine which operates between temperature levels of 927'C and 12

-: -: ' J :;j ec ts 3 0 KJ to the low temperature sink. The heat pump receives 27 0 KJ

- :c:: iiom a low temperature reservoir and rejects it to the surroundings at

-: -:'J Determine the temperature in oC of the low temperature for the heat pump.-_::.'.

3 an expression for an air-standard efficiency for otto cycle. 8

20

L2

I TUR\ O\ ER

M

o

)

5.

: l-1:-liDTn&NK-2-?

Con. 78E2-GX-r2068-13.

(a) Si..r:.1 a: ,i00 kPa having a quality of 0.9 expands adiabatically and reversiblr to ;

^-r:^ai pressure of 100 kPa. Determine its final condition.

rL', -l ie uitimate analysis of a solid fuel is as follows :-

C : 1\oh, Or: 3o/o, Hr: 3oh, S : lo/o, moisture : 5% and ash content : l0o/o

Calculate the mass of air supplied. Also calculate individual and total mass of

products of combustion per kg of fuel if 30% of excess air is supplied for combustion.

5. r a ) In an air-standard dual cycle, the pressure and temperature are 0. 1 mPa and27oC. 12

The compression ratio is 18. The pressure ratio for the constant volume part of

heating process is 1.5 and the volume ratio for the constant pressure part of heating

is 1.2. Determine :-

(i) thermal efficiency.

(ii) mean effective pressure in M Pa. 1,4

State the Clausius clapeyron equation.

Draw a simple schematic of thermal plant with one reheater. Also represent

T:S-diagram

(b)

(c)

n r.i

I.J

-I

4

4

!It.,t

fi

,

{."I "

ts

g-tr | t[ 5trn I fntehl ooec2oL3

.SC CY]

(3 Hours)

Question No. 1 is compulsory.Solve three question from remaining five.Assume suitable data wherever necessary.

Solve any Four Questions ,

Write a short note on Macaulays MethodWhat are the characteristics of bending Moment and What do you mean bypoint of contraflexure.

Provethat fu:r' :u.YIR

What is equivalent length of column ? Give the ratio of equivalent length andactual length of column with various end conditionWhat is the length of 5 mm diameter aluminium wire so that it can be fwistedthrough one complete revolution without exceeding shear stress of 42 MN/m2Modulus of rigidity G= 27 GN/mzDerive an expression for elongation due to self weight of bar

Draw SFD, BMD and AFD for the following beam and also show the point ofcontraflexure if any.

8 kN/nr..- /2LrkN 12 kN

0 kltlm

m

Find the Euler crushing load for a hollow cylinder cast iron column 200 mrnexternal diameter and25 mm thick , if it is 6 m long and hinged at both ends.Take E: | .2 x 105 N/mm? . Compare the load with th'e crushing load as givenby Rankine formula, taking f, =550 N/mm? and a= 1/1600

A cast iron bracket subjected to bending banding has a C/S of I shape withunequal flanges . If the section is subjected to shear force of 120 KN, Drawshear force distribution diagram over the depth of section

GX-12101

ITotalMarks : 80

25:2N half.13-(vlld

Con. 860+13.

N.B.: (l)a)(3)

Q.l.

F

Q.2. A

AB

C

D

Eo

08

10

qln

T:-I

I

3anm

I

II.

1240 r.n

I

J{o rri

20

12

a I TURN OVER

r-l

?1 :2nd half,llAvi(at)

Con. 8604=GX-DLAL -13.

0.75 m

A Hollow shaft with diameter ratio of 3/8 is required to transmit 500 Kw at 100

RPM , the maximum torque b^eing 20 %o greatu than mean. The maximum shear

,t .r, it not exceed 60 Nimm2 and the twist in the length of 3 m is not exceed

I .4 "

Calculate the minimunr diameter required for the shaft . c:84N/mm2

A wooden beam 250mm x 150 mm has a steelstrap 10 mm x 150 mm f,xed at

the top and the bottom. The beam is subjected to bending moment of 5 KN-m

around the horizontal axis . Determine the stress in the steel and wood'

Es:200 GPa" Ew=20 Gpa

A Steel bolt of 20 mm diameter passes centrally through a copper tube of

internal diameter 25 mm and thickness l0 mm . The tube is 600 mm long and is

closed by rigid washer of negligible thickness and fastened by nuts threaded on

the bolt.iinl the stresses in itrJUott & tube when one of the nuts is tightened

by the one quarter of the turn relative to other. The pitch of the thread is 2 mm '

Take E, =200 GPa and E.=100 GPaWasher

Q. 5. A Determine the strain energy of prismatic beam AB for the loading as shown in

10

Q4

10

aliq

-lII

ruT\

II

20

!

07f<.-_--->l750 rnnt

L.25 tti

13

B A horizontal beam is toaded ancl supported as shown in fig ' Determine

(i)Slope at A (ii )P.!::lion and Slope at B (iii) Slope at D20 kN 14 kNlm

F-emmm---l

TURN O\rER

2

27:2rC tutr13+v(4)

Con. 8604-GX-12101=I3- -

':.: C::iposiie bar consisting of steeland aluminium components shown in fig l0Is ctrrnecled to two grip at atemperature of60' C. Find the stresses inther* o roCs, * hen the temperafure , falls to 20' C

( I )lf the ends does not yield(ID If the ends vield bv 0.25 mmiui. , Es=2*rot Nlrn*2, EA = 0.70 x 10s N/mm2'or:l

.I 7 x 10 '5 per 'c s

6:2.34 x l0 '5 per 'c

^..

B A cylindrical shell 800 mm in diameter and 3 m long is having l0 mm metal

thickness. If the shell is subjected to an internai pressure of 2.5 N/mm'Determine (i) The change in diameter

( ii) Ihe chinge in length( iii) The change in volume

Assunre the rnodulus of elasticity and poissions ratio of the material of the shell

rs.200 KN/mm2 and 0.25 respectively

10

rll',/

o

Cc,n. 893-r-13,

3,{l rtt t(ml loeeh lOee 2a3

(3 Hours) t Total I[srks : 80

\.B, : {1,i Question No. 1 is compulsory.(2) Attempt any three questions out of remaining five questions"(3) Figures to right indicate fiill marks(4) Assume suitable data if necessary

L-. L \\'rite short note on any four of following: -

'a) Pattern allowances

- ,b) Thermit welding processer i

(c) Blow moulding process.

1c) Rolling defects.

. e i Important properties of moulding sand. ,

:. : a Explain the process of production of seamless tubes by rolling process.

tl'f'tat is weldabiltiy? Discuss various welding defects with their reriredies.

: \i':r a neat sketch explain the principle of electro slag welding prooess"

Q i a' Sa:ae l'arious methcds of powder manufacture techniques in powder metallurgy and explain

one in detail.

(b) Cmpare TIG and MIG welding process.

(20)

(6)

(8)

(o

c{c} Write short note on application of plastics in industries,

Q.a. (elufiatisNDT-Explain any two NDT methods in detail.

(r) Wie aneat sketch explain the working plinciple of plastic injeition moulding process.

Q5" (a) rie n€d sketches explain briefly on "friction we!ding,,.

(b) A.rs+ftI:g ofS&m x 40cm x 10 cm size solidifrps in 20 minutes. Find the solidification time for{{l cra x 30 cmx 5 cm casing under similar conditions.

(c)Diftmti*ebetween"soldering"and"brazingr'operatioii. :

Q6 (r) ThL thc hcfo of a neat sketch explain the complete gating lystem in casting process.

(b) Dcfine tfie Erms *spread', Tlongation", and "Draft" w.r.t. Rolling process.

(8)

(8)

(4)

(8)

(6)

(o

(o

(8)

(6)

(8)

(6)

(o