IAS Mains Mechanical Engineering 1986

8/20/2019 IAS Mains Mechanical Engineering 1986

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Time Allowed: 3 Hours Maximum Marks: 300

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INSTRUCTIONS

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Candidates should attempt Question 1 and 5 which re compulsory and any ftlie

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remaining question sliecting at least ONE question from each Section. 0

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SEC11 N A

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lt I Answer any three of the following:

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(a) Sketch and describe any mechanism which can give ex

ac

erated straight-Line motion.

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Give mathematical analysis involved.

(b) What is CORIOLIS component of c c e l e r t i o

·, e an expression for evaluating it and

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explain how

the

direction is fixed. '

(c) Discuss the effect of primary, second fot s an couples in a four cylinder in-line four-

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stroke engine with mathematical an · is. m are the above engine with three-cylinder in-

lt line engine in respect ofb alancin .

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(d) From first principles e r i v e sio for the frequency of free damped vibration of a

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single degree freedom with sc dar ping.

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Prove that the amplitude f su 1

ve

oscillations are in geometric progression for

the

above

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2. (a) A wetght W of

~

s

lllg

from a rope wrapped round a drum of effective

rad1us

of 0 3

lt

metre wh1ch IS

tl

t shaft A Shaft A IS geared

to

shaft B which runs

at

6 times the speed

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and

tha

o 1s 5 kgf-m

2

Fmd the acceleration of wetght

W,

1f 1t 1s allowed to fall

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free

he free body diagram of shaft A The configuration of the system 1s shown m

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2/8

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3.

4.

(b)

(a)

T f ~

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:::j· · ·

.

·

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?? ·llJ

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1 L

~

ig.

I

A thm c1rcular

d1sc

1s fitted to a shaft

as

shown m F1g

e

o+ the disc 1s 50

kgf

and

d1ametert s 120

em,

Shaft rotates at

300

r p m m antt-clo · ctton when seen from the

nght

s1de

\ }

Fmd the effect

of

gyro

scop1

c couple

on

the shaft and be · ng reactions at

A

and

B

takmg

the ~ f e t o f w ; ~ ~ h t

of h e = ~ r

~ f l j

. L .

··- ~ L - ·

A L ~

-·1 . - - ~ · ~ ::-_-_. ==-· -: ' . 111

_

...:- \ ~

r'.t. ; . · · • \ \

I

Ar I,..>

1 ~ 0 < . . - - 1 5 < m

h g .2

·

A

single-cylinder

G t i n

pump is driven through gearing at 50 r.p .m.

The

resisting

torque

of

pumpe m 6 assumed to follow a sine curve

in half

revolution with a

maximum value f ~

g -mat 90°

and 270°. Find the weight

of

the flywheel required to be

mounted

on

a pu

~

to keep the speed within

I

Y

of

the mean speed if the radius of

gyration o the flywn eel is

1.5

metre,

The

effect

of

motor armature and gear-wheels is

equ1v t

flyw

heel

of 450 kgf

with a radius

of

gyration

of

I metre on the pump shaft .

(b) ic

ear tram consists

of

a compound gear-wheel CD which gears wtth two mtemal

(a)

wH Is B Gear-wheel C has

30

teeth meshes wtth

mtelnal

wheel A, while D gears

• ' temal wheel B ha111ng 85

teeth Internal wheel

B IS

keyed

to

a shaft L

The

compound

(1)

What

IS

the speed

of

shaft L 1f shaft

M

makes

1000 rpm

and

all

the wheels have the

same p1tch?

(u) What

IS

the load torque

on

the shaft

Land

holding torque

on

wheel

A

1f 1nput torque

(i)

(ii)

to shaft

M

is

8

kgf-m ?

State the theorem

of

Castigliano.

Using the above theorem find the horizontal displacement along the

load

line

of

the

frame shown

in

Fig. 3, considering the deflection due to bending only.

The

moment

of

inertia is the same for all sections

................................................................................................................................................................................................................................................................................................................................................

.


3/8

T

a

Fir-

f

1

t

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(b) A tyre is shrook on a wheel of

12

metres diameter. Asswning the wheel

to

be ri gi

the internal diameter of the tyre, if after shrinking, the hoop stress

in

the tyre is

a for the tyre is

11.7

x

0 6

per °C and E equal

2

x I

0

8

kgflcm

2

.

Find the least

~

J

to

which the tyre must

be

heated above that of he wheel before

it

could be o

SECnONB

~

5. Answer briefly and precisely any three of the following (Each not exceed

200

words):

a) What do you ooderstand by the term 'Cutting Tool : m f ~ ' ? Mention different single

point tool angles and their effect on machining

h

•

ofmetals.

6.

7

8.

(b) What are the princi pies on which forminf l o s are based? How does hydrostatic

extrusion differ from conventional e x t r u s i s Mention the salient points.

c) With reference to quality control, w h d e r s t a n d by the following ?

(d)

a)

(b)

c)

(i) Standard deviation l

(ii)

(iii)

machining methods and mention their areas

of

application.

List out the ~ { Z ; · a in Merchant's theory in orthogonal cutting and draw the force

diagram.

Represent rapht • some of the typical relationships between speed, feed, depth of cut

ce g h n e s s while twning mild steel with sintered carbides and critically

eir relationships.

p nventi on

a

and high velocity forming methods. Discuss the effect of strain and

an1fn velocity on forming methods

c

U are the advantages and disadvantages of having excess inventories ? What are the

ntory policies for

A,

B and C class items ?

l l ~

Deduce an expression for economic order quantity and clearly state the assumptions made

in

the derivation.

(c) The rate of use of a particular raw material from stores is 2 0 units/year. The cost of pi acing

and receiving an order is Rs. 40. The cost of each unit is Rs. I00. The cost of carrying

inventory in per cent per year is 0.16 and

it

depends on the average stock. Determine the

EOQ. f the lead time is 3 months, calculatethereorderpoint.

(a)

(b)

Show how

to

formulate the general linear programming problem of optimal decision -making.

A small plant makes two types of aircraft parts. It buys castings that are machined, bored and

polished. The shop capacity is shown in the table given:


4/8

Castings for Part A cost Rs. 4 each for Part B cost Rs. 9 each; they sell for Rs. 8 and Rs. 18

respectively. The three machines have running costs o

Rs

40

Rs.

28 and

Rs.

35 per hour.

Assuming that any combination o Part A and Part B can be sold what pro duct mix

maximizes the profit ?

Machining capacity

Boring capacity

Polishing capacity

~

Capacities

Part

50

per hour

56 per hour

70 per hour

Part

80 per hour

70 per hour

50 per hour

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5/8

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II

~ A P : R .

•

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Time Allowed: Three Hours Maximum marks: 300

INSTRUCTIONS

Candidates should attanpt Questions 1 and 5 which are compulsory and any T

il i

e

remaining questions selecting t least ON question from each Section

The number

of

marks carried by each question is indicated at the md

of

the ·

I

SEC11 NA

J

Am_,

my

•=

of

0011

Eooh

.

of

..

~

' e .

,

200

~ r o .

' '

a) Explain how the poor takeoff characteristics of turb t en ·nes can be improved by thrust

augmentation.

2

0)

b) Compare the normal pressure and ,

Us

of recipro eating, rotary positive

displacement) and centrifugal c o m

i v e

their relative advantages.

20)

c) A Pitot tube in a wind s tatic pressure reading of 40.7 kgflcm

2

and stagnation

pressure reading of 98 kgfl

2

usp ected that the device used for stagnation temperature

d)

measurement 1s ~ p rature of I0 0

•c

1s recorded If the acoustic vel oc1ty under

the condi tlons

1s

eq)

...

r

m/s

comment on the functlorung

of

temperature measunng

dev1ce {>fj (

2

0)

uss n t g e s and disadvantages of gas turbmes over the reciprocating IC

engme +

20)

e the pressure m the vessel1t 1s connected to an extraction pump The volume flow rate

2

d vessel of volume 0 3 m

3

contams perfect gas at a pressure of I kgflcm

2

In order to

e gas lea111ng the vessel1s constant at 0 014 m

3

/mm Assummg the temperature of the gas

to reman

constant, calculate-

b)

1)

time taken on reduce to pressure m the vessel

to

0 35 kgflcm

2

,

u) magmtude and sense

of

heat transfer between the vessel and the surroundmg dunng

the time.

Derive any formula you use.

30)

kg/s of air at 20 o•c flowing through a pipe at I 00 m/s is mixed adiabatically with I kg/s of

air at 100°C which is following through another pipe at 50 m/s. The resulting mixture flows

at a pressure

of

4 kgflcm

2

in a pipe

of

I 0 em diameter. Determine the temperature and

velocity

of

the mixture.

£

:;


6/8

3. (a)

(b)

4

(a)

(b)

(Assume that Cp 0.27 kcallkg-K and

R 29.2 kg-mlkg/K)

(30)

A boiler has a volume of I 0 m

3

and contains water in liquid and vapour phases at 3 0 kg/cm

2

pressure. Initially the liquid phase occupies half the volume. Fluid may be allowed to escape

from the boiler by two valves one at the top of the boiler and the other at the bottom. Heat is

transferred to the boiler at such a rate that the temperature

of

the fluid remains constant. Find

the amount of heat which must be transferred if 3 0 0 kg of fluid are allowed to escap via (i)

upper valve (ii) lower valve. It may be assumed that no liquid particles are held in s ~

in the vapour. '

(30)

A multistage gas turbine is to be designed with impulse stages and is to ~ an inlet

pressure and temperature of 6 kgflcm

2

and 900 K

r e s p e c t i v e l y

s s u r e

is I

kgflcm

2

and 900 K respectively. The outlet pressure is I kgflcm

2

. isen pte efficiency of

the turbine is likely to

be

8 5 . All stages are to have a nozzle outlet

a 15°,

equal

in et,

and outlet blade angles, a mean blade speed of 250 m equal mlet and outlet gas

velocities. Estimate the number of stages required. Assu

e

~ kcallkg-K and

y

Any datanot given can be assumed sui table.

1.333.

J

(30)

Calculate the power required for two m f t e : s

~ l

ammonia system that serves a 3

0-

tonne evaporator at -2 8.9°C. The syst a illrect contact cascade condenser, and the

condenser temperature is 37.8 •c The o

~ v a l u e s

or ammonia are available:

Pressure kgf cm

2

4.13

14.00

-28.9

0.56

37.8

48.9

87.8

Enthalpy lccallkg

376.9

386.6

150

424.4

(2) Saturated Ammonia

Saturation Press

kgf cm

2

1.3772

1.27

1.3772

Enthalpy krallkg Entropy{Vapour)

lccallkg-K

h

336

345

351.6

h

119

43.7

86.2

1.3772

1.27

1.171

If instead of two-stage compression a single-stage is used calculate the power required. Also

compare the COP of one-stage and two-stage systems.

(35)

A room

7m

x

4m

x

4m

is occupied by an air-water vapour mixture at 38°C. The atmospheric

pressure is I kgflcm

2

and the relative humidity is 70 Determine the humidity ratio, dew

point, mass of air and the mass of water vapour. If the mixture of air-water vapour is further


7/8

5.

cooled at constant pressure until the temperature is

10•c,

find the amount

of

water which

condensed.

Assume

R

- - - L .

0.622

and R r

29.2

kg-mlkg-K

R.,p,..

(25)

SECnON

Answer any three

of

the followmg four parts (answer to each part should not exceed 200

a) 1)

Show that for an

1deal

gas wtth constant heat capacities, the slope o

~ f o r

a

revers1ble ad1abat1c pro cess 1s negative and that

1t

has larger absolute v u than the

slope

of

a P-V curve for an Isotherm at the same value

of

P ant

(I

0)

b)

(c)

d)

(u)

A thermometer

1s

mserted m a p1p

e

through which

1s

flowtng a y stream

of

gas

at

a temperature

T1

and velocity

u1.

Will the i n d i c a t e d

be higher than, lower

than or same as T

1

?

'

(10)

Explam the purpose of usmg regenerative plant. Outline a method for

optimum heater lo catlon How does a reheat.,rv tlve cycle differ from regenerative

1)

Prove that system energy 1s pert)

(I

0)

(u) Prove that

ds c

d

T

~

(I

0)

formation of carbon depo s1ts and smoke m gas turbine

om u s t l ~ chamber ?

(I 0)

6.

Explam the term cntlcal msulatlon th1ckness A small electnc heating apphcatlon uses

0 183

em

diameter wtre wtth 0 071 em thick msulatlon The thermal conduct:1111ty of the

insulation is 0.1

015

kcal/m-hour

•c

and surface convection beat transfer coefficient is

29.3

kcal./m

2

-hour

•c

Calculate the critical thickness of the insulation and the effect of employing

critical insulation thickness. Assume that the temperature difference between the surface of

the -wire and surrounding air remains unchanged. Derive the formula used.

(30)

b)

In a long tube

of

outer radius r

0

is insulated

at

its outer periphery. The tube is cooled at the

inner radius r

1

. Uniform heat generation

at the

rate

of

q occurs within the solid walls

of

the

tube.


8/8

7 a)

b)

c)

8. (a)

b)

(i) Find a general soluti on for temperature distribution

in

the tub

e

(The maximum

permissible temperature at the insulated

surf cer

r

0

is T

0

.

(ii) Heat removal rate.

Assumptions, if any, be stated clear

y.

(30)

For flow

of

a liquid metal through a circular tube, the velocity and temperature profiles at a

particular axial location may be approximated

as

being uniform and parabolic respectively.

What

is

the value

of

Nusselt number at this location

? 2 0)

1)

(ii)

v 15.36 x 10-6m

2

/s,

Pr 0.709

(30)

Show by d1menr st s

th t

for turbulent flow m rough p1p

es

the res1stance coeffic1ent

f

1s

a funct1on o y ,

Jd

number and the ratio

Rfk

where

R

1s

the p1pe radius and k

1s

the

average he1ght o " ughness

proJ

ectlons on the wall

of

he

p1p

2 0)

Den

for spec1fic speed

of

a turbme m terms

of 1ts

speed

N,

output power P

ectnc station the avatlable head 1s 6 0 m and

1t 1s

anticipated that

32

3 m

3

/s

of

t wtll be avatl able Franc1s turbmes

of sp ec1fic

speed

of

19

0 ate to be mstalled and are to

0 0 r p m wtth an overall efficiency

of

8 2% Detemune the maxtmum power avatlabl

m the turbmes and the number reqwred

2 0)

Discuss the various mechanisms

of

heat transfer

th t

take place

when

a red

hot

steel is

quenched

in

a brine sol uti

on

at atmospheric temperature till the steel attains the temperature

of

he brine solution. Sketch the same on a heat flux-temperature diagram. (20)

Documents

IAS Mains Mechanical Engineering 1986