MECHANICAL ENGINEERING Paper—II

Q. Derive the optimum pressure ratio of an ideal gas turbine plant for maximum network.
Also, show with the help of T-s diagram that, an optimum pressure ratio exists. 10

Q. Consider one-dimensional isentropic flow of a perfect gas. Derive an appropriate expression
to show that the shape of the nozzle for supersonic flow is divergent in cross-section.10

A small sphere (of outside diameter 60 mm) with a surface temperature of 300°C is
located at the geometric centre of a large sphere (of inside diameter 360 mm) with an
inner surface temperature of 15°C. Calculate how much of emission from the inner
surface of the large sphere is incident upon the outer surface of the small sphere. Assume
that both bodies approach black body behaviour. What is the net interchange of heat
between the two spheres 10

Q. Steam at atmospheric pressure enters the shell of a surface condenser, in which the water
flows through a tube bundle, at the rate of 0.05 kg/s. The inner diameter of the tube is
25 mm. The overall heat transfer coefficient, based on the inner diameter is 230W/m2oC.
The inlet and outlet temperatures of water are 15°C and 70°C, respectively. The condensation
of steam takes place on the outside surface of the tubes.

Calculate the following

The effectiveness of the heat exchanger and NTU.
Length of each tube.
The rate of steam condensation.

Assume Cp of water 4.18 hfg 2 2 5 7 (latent heat of condensation). 10

Q. Propane (C3H8) is burned with 100% excess air in an adiabatic burner. Both the fuel and
air enter the burner at 25 °C and 1 bar. Estimate the maximum temperature that can be
attained in the flame. The molar heat capacities of the product gases are as follows

19.8 7.344 x T
32.24 1.924 x 10“3 T
28.11 3.68 x KT6 T
Cp(N2) 31.15 1.357 x T
Here C° is in J/mol. K and T is in K. Assume standard heat of this reaction
as AH29g -2045.5 kJ. 10

Q. Explain what do you mean by kinetic energy correction factor. Show that the kinetic
energy correction factor for laminar flow through a circular pipe is 2. Further, explain
what will happen to the kenetic energy correction factor when the flow is considered to be turbulent.

Q. A plane wall 90 mm thick 0.18 is insulated on one side while the other side
is exposed to environment at 80°C. The rate of heat generation within the wall is
1.3 x 10?5 W/m3. If the convective heat transfer coefficient between the wall and the
environment, is 520 W/m2oC, determine the maximum temperature in the wall. Derive
the expression used, starting from the steady state one-dimensional heat conduction with
heat generation equation.

Q. Show that the slope of a reversible adiabatic process on a temperature versus pressure
diagram, when multiplied by Cp is given by Tvp. 10

Q. A centrifugal compressor running at 16,000 rpm takes in air at 17°C and compresses it
through a pressure ratio of 4:1 with an isentropic efficiency of 82%. The blades are
200 mm and the absolute air velocity at inlet is 120 m/s. Calculate the impeller tip
what will happen to the kinetic energy correction factor when the flow is considered to
be turbulent. 20
radially inclined and the slip factor is 0.85. Guide vanes at inlet give the air an angle of
pre-whirl of 20° to the axial direction. The mean diameter of the impeller eye is
diameter. Take Cp 1.005
impeller exit. 20

Q. A nine (9)-cyIinder, 4-stroke petrol engine of bore 14.5 cm and stroke 18 cm, has a
compression ratio of 7:1 and develops 350 kW at 2000 rpm when running on a mixture
of 15% weak. The fuel used has a heating value of 47 MJ/kg and contains 85.2% C and
14.8 H2. Assuming a volumetric efficiency of 76% at 15°C and 1 bar and mechanical
efficiency of calculate the indicated thermal efficiency of the engine. Given,
R 287 J/kg-K. 20

Q. A boiler furnace of 3 m height is made in the shape of a frustum of a cone with the
bottom diameter 5 m and top diameter 6 m The emissivity of both the surfaces
is 0.9. The bottom surface is at 1000°C and the top surface is at 500°C. Considering the
inclined surface is refractory surface, find the radiation heat transfer from the bottom
to top surface and the inclined surface temperature. Radiation Shape Factor
F1_2 0.4. 10

Q. A 2-stroke motor cycle petrol engine cylinder consists of 15 fins on its outer surface. If
the outside and inside diameters of each fin are 200 mm and 100 mm respectively, the
average fin surface temperature is 475°C and the atmospheric air temperature is 25°C,
calculate the heat transfer rate from the fins for the following cases

when the motor cycle is stationary;
when the motor cycle is running at a speed of 60 kmph.

The fin may idealized as a single horizontal plate of the same area, and the significant
length may be taken as L 0.9 d0, where d0 is the outer diameter of the fin. Assume d0
as 200 mm.

The properties of air may be takenas follows
k 4.266 x v M M x 10”6 Pr 0.677
For turbulent flow (forced convection^ Nu » 0.036 8
For natural convection

Nu 0.54 (Gr. if (Gr. Pr) 109
Nu 0.10 (Gr. Pr)0 33 if (Gr. Pr) 109 20

Q. A gas turbine operating on actual simple Brayton cycle is to be designed for maximum
output. If the maximum and minimum temperatures of the cycle, the efficiencies of
compressor and turbine are fixed, derive the expression for optimum actual pressure ratio.
What will be the value of optimum pressure ratio for turbine, if the ratio of maximum
and minimum temperature is 3 and y 2

Take efficiencies of turbine and compressor as 0.9 and 0.8 respectively. 20

Q. Explain what do you mean by Highest Useful Compression Ratio (HUCR) for S.I. engines
and also state its importance. 10

SECTION—B

Q. Justify the suitability of thermostatic expansion valve in comparison to automatic expansion
valve. 10

Q. Explain with a neat sketch, how air charge, air consumption, torque and mechanical
efficiency vary with the range of speed in I.C. engines. 10

Q. A steam power plant, working on Rankine cycle has constant steam temperature. The
condenser pressures are 25, 50 and 75 mm of Hg and inlet steam pressure varies
from 20 to 160 bar. Explain with the help of performance curve and reason how the
thermal efficiency will vary.

Which are the factors effecting Nozzle efficiency 6+4

Q. Air flows in a circular duct which suddenly contracts in the cross sectional area. Draw
the flow sketch and locate the points on the sketch where turbulent flpw will occur and
calculate the dynamic loss co-efficient. Take the co-efficient of contraction as 0.62.10

Q. What is an Orsat apparatus Draw a neat diagram of Orsat apparatus and explain its
functioning. 10

Q. In a drier operating at steady state atmospheric air at 30°C and 101.325 kPa wth a
relative humidity of 40% is first heated to 110°C at constan pressure. The heated mr s
then allowed to pass over the material to be dried and the air leaves the drier at 70 C with
a relative humidity of 0.5. If it is required to remove 60 kg/mm of moisture from t e
material, determine the mass flow rate of dry air required in kg/min and the rate
transfer to the air as it passes through the heating unit. Use hg'“ c 2696.12 kJ/kg.on


PSYCHROMETRIC chart
BAROMETRIC PRESSURE 1.01325 bar
SEA LEVEL
VOLUME, m3/kg
0:90 mVkg
DRY AIR
Do not write your Roll No.
on this Sheet
0.75 ma/Xg 0.80 m3/kg
BELOW 0*C PROPERTIES AND ENTHALPY DEVIATION LINES ARE FOR ICE
0.85 m3/kg
SPECIFIC
0 .3 5
0.032
0.029
0.028
0.026
0.025
0.024
C.023
0.022
0.021
0.020
0.019
0.016

. 3 0
0 .4 5
£E
• 0 .5 0 roO*
£
0.55 £
UJ
X
1U
• 0 .6 0 3 2S
0 .6 5 Z
iO
-C.70
0.7S
¦o.ao
0 .8 5
0 . 9 0
¦0.95
•1.00
009
008
Ref. Point for S.H.F. 25°Q, 50% R.H.

Q. The angles at inlet and discharge of the blading of a 50% reaction steam turbine are 35°
and 20° respectively. The speed of rotation is 1500 rpm and at a particular stage, the mean
ring diameter is 0.67 and the steam condition is 1.5 bar, 0.96 dry. Estimate the
required height of blading to pass 3.6 kg/s of steam, and the power developed by the
ring.

Assume, at 1.5 bar pressure, vf 0.001052— and vfo, 1.15937— . 20
kg Ig kg

Q. What are the functions of condenser in a refrigerating machine Name different types of
condensers. Describe with neat sketch the evaporative condenser. 10

Q. A refrigerating machine, rated to produce 40 tons of refrigeration, is used for air conditioning
between the; operative temperatures of 42° and 6°C of condenser and evaporator respectively.
The refrigerant is dry saturated at the end of compressor. Find the capacity of the plant,
power and capacities of compressor and condenser.
Properties of refrigerant
Temp.

Pressure
bar
Enthalpy Entropy Volume
"r sf S8
42 1.957 249.7 410.7 1.125 1.6712 0.6975
6 0.5160 407.15 1.018 1.687 0.04035
-32 0.0875 390.85 0.9178 1.715 0.1665
If the evaporator’s temperature is reduced to what will be effect on capacity of
plant, power and capacities of compressor and condenser 20

Q. Differentiate between normal and abnormal combustion in SI engines. List out the three
major knock limited parameters and explain its use in the engine design. 10

Q. 7(c)Dry saturated steam at 5 bar enters a convergent-divergent nozzle at a velocity of
100 m/s. The exit pressure is 1.5 bar. The throat and exit areas are 1280 mm2 and
1600 mm2 respectively. Assuming isentropic flow upto the throat and taking the critical
pressure ratio as 0.58, estimate the mass flow rate. If the nozzle efficiency is 0.973,
determine the exit condition of steam dryness fraction. Show the process on T-s and
h-s diagrams.

Properties of Steam
p

Enthalpy Entropy (kJ/kg Volume
fg sf sfg vf vfg
5.0 640.23 2108.5 l.8607 4.9606 0.00109 0.3708
2.9 556 2 168 l.660 5.344 0.00107 0.6253
l.5 467.11 2226*5 1.4336 5.7897 0.00105 1.158
20

Q. In a cogenerationrplant, the power load is 5.6 MW and the heating load is 1.163 MW.
Steam is generated at 40 bar and 500°C and is expanded isentropically through a turbine
to a condenser at 0.06 bar. The heating load is supplied by extracting steam from the
turbine at 2.0 bar, which is condensed in the processor device to saturated liquid at 2.0
bar and then pumped back to the boiler. Compute, the steam generation capacity of the
boiler in kg/hr, the heat input to the boiler in kW, the fuel burning rate of the
boiler in if a coal of calorific value 25 MJ/kg is burned and the boiler efficiency is
88 the heat rejected to the condenser the rate of flow of cooling water in the
condenser if the temperature rise of water is 6°C. Neglect pump works. Draw the T-s
diagram. Properties of steam At 40 bar 500°C.

v 0.08643 m3/kg, h 3445.3 kJ/kg, s 7.0901 kJ/kgK.

Psnt

Volume Enthalpy Entropy
vf vg hf sf sg
2.0 0.00106 0.8857 520.72 2712.1 1.5706 7.0878
i
0.06 0.00101 25.22 149.79 2565.79 0.520 8.335
20

Q. 8 Discuss the lubrication of the following engine paFts with the help of neat sketches
Main bearings
Cylinder and small end bearing of connecting rod
Crank and Gudgeon pin. 15

Q. 8 Explain with a sketch how heat is absorbed at various stages from feed water to steam
generation in water tube boilers. 15