8/20/2019 IAS Mains Mechanical Engineering 1986
1/8
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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
lt All question carry equal marks.
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SEC11 N A
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lt I Answer any three of the following:
D
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(a) Sketch and describe any mechanism which can give ex
ac
erated straight-Line motion.
lt
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
lt
explain how
the
direction is fixed. '
(c) Discuss the effect of primary, second fot s an couples in a four cylinder in-line four-
lt
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
lt
free
he free body diagram of shaft A The configuration of the system 1s shown m
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' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ~ ·
3.
4.
(b)
(a)
T f ~
I
- .
:::j· · ·
.
·
I ;
?? ·llJ
i.J. .
{
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
................................................................................................................................................................................................................................................................................................................................................
.
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T
a
Fir-
f
1
t
I
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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:
8/20/2019 IAS Mains Mechanical Engineering 1986
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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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Ja·
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II
~ A P : R .
•
i i
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.
£
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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
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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.
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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)
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