ARUNACHAL PRADESH PUBLIC SERVICE COMMISSION ITANAGAR
SUBJECT: MECHANICAL ENGINEERING: PAPER
Time: 3 hours Full Marks: 200
Note: Answer Question No.1 and any four from the rest. All questions carry equal marks.
Q. No.1. Attempt any 10 10x4 =40
a.
What is the zeroth law of thermodYnamics?

b.
Work is a path function. Explain.

c.
What is a perpetual motion machine of the first kind?

d.
What is a quasi-static process?

e.
Give the Clausius statement of the second law ofthe thermodynamics.

f.
What is entropy principle?

g.
What are boiler mountings? Give at least th'ree examples.

h.
Explain the difference between single 'acting and double acting steam engines.

i.
Why steam nozzles are made convergent-divergent?

j.
What are the disadvantages of ana,bsorption' refrigerant system over a vapour compression. refrigerant system?

k.
Find the loss of head when a pipe of 200 mm is suddenly enlarged to diameter of 400 mm. The rate of flow of water through the pipe is 250 Iitres per second.

I.
A hydraulic turbine develops 9 MW when running at 10 rpm. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 determine the power developed by the turbine.

Q.
No.2. Attempt any 8 (eight) 8 x 5 40

a.
A platinum resistance thermometer has a resistance of 2.8 ohm at OOC and 3.8 ohm at 1000e. Calculate the temperature when the resistance indicated is 5.8 ohm.

b.
The following data refer to a 12 cylinder} single acting two stroke marine diesel engine: Speed =150 rpm} cylinder diameter =0.8 stroke of piston =1.2 area of indicator diagram =5.5 x


2
10-4 m length of diagram =0.66 spring value =147 MPa per m.
Find the net rate of work transfer from the gas to the piston in kW.

c.
A stationary mass of gas is compressed without friction from an initial state of 0.3 m3 and 0.105 MPa to a final state of 0.15 m3 and 0.105 MPa, the pressure remaining constant during the process. There is a transfer of 37.6 kJ of heat from the gas during the process. How much does the internal energy of the gas change?

d.
A cyclic heat engine operates between a source of temperature of BOOoC and a sink temperature of 30°C. What is the least rate of heat rejection per kW net output of the engine?

e.
Show that the change in entropy of an irreversible process is always positive.


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f.
Compare a four stroke IC engine with a two stroke one.

g.
A gas fired refrigerator operates between two thermal energy reservoirs -one at 273 K and the other at 300 K. If the ambient temperature is 300 determine the maximum COP possible.

h.
The conditioning system of a room is required to deliver air at 290 K having 60% relative humidity. Determine the specific humidity.

i.
Explain briefly the working principle of Bourdon Pressure Gauge with a neat sketch.

j.
A body of dimension 1.5 m x 1.0 m x 2 m weighs 1962 N in water. Find the weight in air. What will be its specific gravity?

Q.
No.3. Attempt any 5 (five) 5 x 8 =40

a.
Describe the Bomb calorimeter with a neat sketch. Explain in brief how the calorific value of a solid fuel is determined using it.

b.
Give the classification of steam turbines. Explain each type with simple diagrams.

c.
What do you mean by governing of IC engines? Briefly explain the different methods employed for governing.

d.
What are the major and minor energy losses in pipe flow? How tbese losses are estimated?

e.
Prove that the work done per second on a series curved vanes by a jet of water striking at one of the tips of the vane is given by


pal{.[VW1 tl
Where it cross-sectional area of the jet, V1=velocity of jet, it =velocity of vane! Vw1, Vw2 =velocity of whirl at inlet and outlet.
f.
Derive an expression for the specific speed of a hydraulic turbine.

g.
Prove that the mean temperature difference in a parallel flow heat exchanger is given by


9.
r· 01
Llrri:l'
i"

.,Dl:J
g B
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Q. No.4. Attempt any 4 (four) 4 x 10 40
a.
Show that the internal energy is a property of the system.

b.
Show that the COP of a heat pump is greater than the COP of a refrigerator by unity.

c.
Prove that the heat flow through the hollow cylinder is given by






where T1 R1, R2 are outside and inside radii, K is the conductivity of the cylinder material, L is the length of the cylinder.
d.
The power P required to run a centrifugal pump depends on the impeller diameter the rotational speed the rate of discharge density p and viscosity Using Buckingham's IT theorem! obtain an expression for the power.

e.
Derive an expression for the minimum speed for starting a centrifugal pump.


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Q. No.5. Attempt any 2 2 x 20 =40
3

a. A vessel of volume 0.04 m contains a mixture of saturated water and saturated steam at a temperature of 250°C. The mass of liquid present is 9 kg. Find the pressure, the ,mass, the specific volume, the enthalpy, the entropy and the internal energy. The steam properties 250°C (saturated pressure 3.973 MPa) are given as follows:
Vf= m3/kg, vg=0.05013 m3/kg
hf 1085.:36 kJ/kg, hfg =1716.2 kJ/kg
Sf 2.7927 kJ/kg K Sfg 3.2802 kJ/kg K

b. A single stage double acting air compressor of 62.5 kW IP at 120 rpm takes air at 1 bar and delivers at
35
10 bar. Assuming the law of expansion and compression as pV1. constant, find the diameter and stroke of the cylinder. Take piston speed 200 m/min, volumetric efficiency 90%. Also find the clearance volume as percentage of stroke volume.
c.
single acting reciprocating pump has a plunger of 100 mm diameter and a stroke of length 200 mm. The centre of the pump is 4 m above the water level in the sump and 14 m below the level of water in a tank to which water is delivered by the pump. Thediameter and length of suction pipe are 40 mm and 6 m while the delivery pipe are 30 mm and 18 m respectively. Determine the maximum speed at which the pump may be run without separation, if separation occurs at 7.848 N/cm2 below the atmospheric pressure. Take atmospheric pressure head 10.3 m of water.

Q.
No.6. Attempt any 4 (four) 4 x 10 =40

a.
Prove that if a reversible heat engine has to operate in a cycle to give same net work output, it must operate between two temperature limits T1 and T2 (T1

b.
A certain mass of gas in a closed system is undergoing polytropic expansion in accordance with the expression PVn constant. It takes Ql-2 amount of heat in the course of its change of state from 1 to 2. Show that




.
tii X Polytropic work done
c. Show that the air standard efficiency of an Otto cycle is given by





.
Tk
where rk= compression ratio, Y specific heat ratio
d. Show the maximum discharge of steam through a nozzle takes place when the ratio of steam pressure
at the throat to the inlet pressure is given by




,Pi -t·1·"
e.
Derive Bernoulli's equation for the flow of an incompressible frictionless fluid from consideration of momentum.

Q.
No.7. Attempt any 2 2 x20 =40

a.
During a trial on a single cylinder double acting non-condensing steam engine running at 250 rpm, the following readings were taken: Cylinder diameter 26 cm Piston rod diameter 5 cm Engine stroke 36 cm Cut-off 1/3 of the stroke Base of indicator diagram 5.2 cm Area of indicator diagram for head end crank end 15.625 cm2 14.375 cm 2 respectively Spring strength 12 N/cm2/cm . Circumference of the brake wheel 5.3 m Circumference of the brake rope 6.2 cm Dead load on brake 2000 N Spring balance reading 200 N Pressure of steam supplied 10 bar Dryness of steam supplied =0.9 Find Indicated Power, Brake Power and Mechanical Efficiency

Specific steam consumption on IP BP basis
. Brake Thermal Efficiency x2 3 x2


b.
The following data refer to a Pelton wheel: ..
Generator output 5000 kW



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A.E.(EIecl)-2012jMechanicai Engg. pol


Head =400m
Generator efficiency 95%
Overall efficiency 85%
Coefficient of velocity 0.98
Speed ratio 0.46
Jet ratio 10
Number of poles= 12
Determine quantity of water required

diameter of jet
diameter of runner
synchronous speed 6 20)
c. An ideal SI engine operatiQg in an Otto cycle intakes air at 290 K/l bar and compresses it adiabaUcally to 15 bar, which reaches 40 bar at the end of heat addition stage. Calculate the

Air standard efficiency


Compression ratio


Mean effective pressure
Net work output for the cycle (4 x5
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