CS MAINS
MECHANICAL ENGINEERING (PAPER-II)
ITime Allowed Three Hours I IMaximum Marks: 250 I
QUESTION PAPER SPECIFIC INSTRUCTIONS
(Please read each of the following instructions carefully before attempting questions)
There are EIGHT questions divided in two Sections and printed both in HINDI and
in ENGLISH. .
Candidate has to attempt FIVE questions in all.
Question Nos. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted
choosing at least ONE question from each Section.
The number of marks carried by a question/part is indicated against it.
Answers must be written in the medium authorized in the Admission Certificate which must
be stated clearly on the cover of this Question-cum-Answer Booklet in the space
provided. No marks will be given for answers written in medium other than the authorized
one.
Wherever any assumptions are made for answering a question, they must be clearly indiCated.
Diagrams/figures, wherever required, shall be drawn in the space provided for answering the
question itself.
Unless otherwise mentioned, symbols and notations carry their usual standard meanings.
Attempts of questions shall be counted in chronological order. Unless struck off, attempt of a
question shall be counted even if attempted partly. Any page or portion of the page left blank
in the Question-cum-Answer Booklet must be clearly struck off.

I SECTION-A
1. In a Carnot cycle, heat is received at 480°C and rejected at 40°C. The entropy of the sink increases by 0.0785 kJ/kg K per cycle. Determine the work done per cycle. 10
An open-cycle gas turbine plant with turbine efficiency nt has a compressor of
efficiency nc, The minimum gas temperature is Tmin and after heating in the
combustion chamber, its temperature is Tmax . If the pressure ratio for
compression and expansion is rp, what should, be the limit for the product
nc.nt.Tmax/Tmin?

Neglect pressure losses and assume that working substance is a perfect gas.

Derive the following expression for normal shock in an ideal gas
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where x and y are conditions before and after the shock, y is ratio of specific heats and M is Mach number. 10

A thin radiation shield having equal emissivities on both sides is introduced parallel to and in between two large planes with emissivities 0.8 and 0.5 respectively. Determine the emissivity of the radiation shield to reduce the heat transfer rate by 92% of the original. 10


The outer and inner surfaces of a thick hollow cylinder have areas 1.25 m2 and 0.25 m2 respectively. The thickness of the cylinder is 10 cm and the thermal conductivity of the cylinder material is 50 W/m K. Find the radial heat transfer through the cylinder for 100 °C temperature difference at the surfaces. Derive the formula used. 10
2.
A reciprocating air compressor is used to fill rapidly a 3 m3 tank at 30°C and 1 bar. The filling process is governed by pv1.4 const. The effects of kinetic energy are negligible. The ratio of the final to initial mass of air in the tank is 4.
Work out the following

Draw the system and show the control volume.
List the assumptions made.
What would be the work input to the compressor, if mechanical efficiency
is 20

A centrifugal compressor running at 1200 r.p.m. delivers 800 m3/min of free air. The air is compressed from 1 bar, 30 °C to 4.8 bar with isentropic efficiency of 0.84. The impeller blades are radial at outlet and the flow velocity of 80 m/s may be assumed constant throughout. The outer radius of the impeller is twice the inner. The slip factor may be assumed as O·9. The blade area coefficient is equal to o·9 at inlet.
Draw inlet and outlet velocity triangles for the impeller, and show the process on a T-s diagram. 3 IP.T.O.
Calculate the input power needed, if mechanical efficiency is 95%.
Calculate the impeller diameters at inlet and outlet.
Calculate the impeller and diffuser blade angles at inlet. 20


The vapour, at the saturation temperature of an oil flowing at the rate of 500 kg/min, enters a heat exchanger tube, at 355 K and condenses while it is cooled by water flowing at the rate of 3600 kg/min entering the concentric tube of a parallel-flow heat exchanger at 286 K. Assuming overall heat transfer coefficient of 475 W/m2 latent heat of oil as 600 kJ/kg calculate the number of tubes required of 25 mm outer diameter and 2 mm thick with a length of 4.87 m. What will be the number of tube passes, if cooling water velocity should not exceed 2 Take Cp for water as 4.18 kJ/kg K and density of water as 1000 kg/m3. 10

3. fa)
Using Buckingham's pie theorem method, derive a relation for the efficiency n of
a fan which depends on the following parameters
Mass density Dynamic viscosity mue, Angular velocity Diameter of the rotor Discharge Q 20

Two long slender rods A and made of different materials having same diameter of 12 mm and length 1 are attached to a surface maintained at a temperature of 100°C. The surfaces of the rods are exposed to ambient still air at 20 °C. By traversing along the length of the rods with a temperature sensor, it is found that the surface temperatures of rods A and B are equal at positions 15 cm and 7.5 cm respectively away from the base surface. If material of A is carbon steel with thermal conductivity 60 W/m what is the thermal conductivity of rod List the assumptions made. Assume that the average convection coefficient for air is 5 W/m2K. Find the ratio of rate of heat transfer for rods A and B. 20

A certain amount of gas is filled in a tank X until its pressure is 100 kPa and temperature is 330 K. In another tank 5 times the weight of gas in X is filled raising the pressure to 500 kPa and temperature 900 K. Both the tanks X and Y are now connected through a tube having a valve which is closed. Assuming the gas is ideal and if the valve is opened till equilibrium state is achieved. find the ratio of the volumes of both tanks, equilibrium temperature and pressure. The tanks are insulated. For the gas, take R 0.296 kJ/kg K and Cv 0.75 kJ/kg K. 10
4.
Liquid N2 enters a thin-walled 20 mm diameter tube at 77 K and flows steadily. The outer surface of the tube has an emissivity of 0.02. This tube is placed concentrically in another tube of 50 mm inner diameter, whose inner surface emissivity is 0.05. The inner surface of the outer tube is maintained at 300 K and the space in between the tubes is evacuated. Determine the heat gained by the liquid N2 per unit length of the tube. If a thin-walled radiation shield with emissivity 0.02 on both sides is inserted midway concentrically between inner and outer tubes; calculate the change in heat gained by liquid N2 per unit length of the tube. 20

Afluid flowing in a tube at the rate of O.5 kg/s is heated from 30 DC to 60 DC by hot gases entering at a temperature of 180 DC and leaving at 80 DC. The specific heats of the fluid and gases are 4.186 kJ/kg Kand 1.08 kJ/kg K. Calculate the change in entropy and increase in unavailable energy for ambient temperature of surrounding of 20°C. 20

In a simple open-cycle gas turbine plant, air enters at 1 bar, 288 K and is compressed to 2 bar. It is then heated in the regenerator before entering the combustion chamber where it is heated to a temperature of 1700 K and then enters, a turbine and expands to atmospheric pressure. The isentropic efficiencies of compressor and turbine are 87% and 88% respectively. The combustor and heat exchanger efficiencies are 0.97 each. Pressure loss in the combustor is 0.4 bar. Power developed by the turbine is 350 MW. Calorific value of fuel is 42 MJ/kg. Assume CPair CPgas 1.005 kJ/ kg K and y(gaama) 1.4.
Draw the system flow diagram and show the processes on a T-s diagrm.
Find out the mass flow rate of air and fual.
Find out the work ratio.
Find out the thermal efficiency.
Find out the special fuel consumption.

I SECTION-B
5. The products of combustion of an unknown fuel CxHy have the following composition as measured by an Orsat apparatus:
CO2 CO 02 N2 82.3%
Detennine the values of x and the air-fuel ratio and of excess air used. 10
Determine the expression for the ratio of chimney gas temperature to outside air temperature in terms of mass flow rate. 10
At a stage in a reaction turbine, the pressure of stearn is 34 kPa (vg =4.65 m3/kg) and dryness fraction is 0.95. For a flow rate of 36000 kg/hr, the stage develops 950 kW. The turbine runs at 3600 r.p.m. and velocity of flow is 0.72 times the blade velocity. The outlet angles of both stator and rotor blades are 20°. Detennine at this stage the mean rotor diameter and height of blades. 10
Mechanical air-conditioning can be used in all geographical locations, whereas desert air-coolers can be used only in some geographical locations. Explain why. Show the processes involved in both these equipments. 10
It is thermodynamically advantageous to employ a heat pump rather than employing a direct electrical resistance heater for a room air heating application. Explain why. 10

6. A 2-stroke oil engine was subjected to a test at room temperature of 20 DC with fuel oil of calorific value 44000 kJ/kg. Calculate the indicated and brake power, mechanical and brake thermal efficiency, and draw the heat balance sheet using the following data

Cylinder bore 20 cm; Stroke-bore ratio 1.3 Speed 500 r.p.m.; Brake drum diameter 120 cm; Rope diameter 3 cm; Net brake load 460 Indicated MEP 2.8 bar; Oil consumption 3.7 kg/hr; Jacket cooling water rate 456 kg/hr with a rise in temperature of 27 DC; Exhaust gas temperature entering calorimeter is 320 DC and leaving 220°C; Temperature rise in calorimeter water is 8 DC with a rate of flow 8 kg/min


In a combined gas turbine (GT)-steam turbine plant, the exhaust from GT is used to heat steam in boiler at which a further supply of fuel is burned in the gas. Pressure ratio of GT is inlet air temperature is 15°C, maximum cycle temperature is 800°C. Combustion in boiler increases the gas temperature to 800 °C and gas leaves the boiler at 100°C. The steam inlet in ST is at 60 bar and 600°C 3656'2 kJjkg, s 7·166 kJjkg and condenser pressure is 0·05 bar (hf 137.8 kJ/kg, hfg 2423.8 kJ/kg, sfg 0.476 kJ/kg Sfg 7·92 kJ/kg K). Calculate flow rate of air and steam required for a total power output of 190 MW and the overall n of the combined plant. Assume that all processes are ideal. What is overall air-fuel ratio? Assume Cpgas 1·11 kJ /kg K gas and Cpair 1.05 kJ/kg and y for gas and air as 1.33 and 1.4 respectively. Neglect mass flow rate of fuel on the airflow. Calorific value of fuel is 43.3 MJ/kg. 20


Show that the enthalpy of humid air per kg of dry air is given by h Cpm xDBT +2500w where CPm humid air specific heat (1.005 1.88w), w specific humidity kg/kg of dry air, hfg 2500 kJ/kg at 0 °C for water and DBT dry-bulb temperature. 10
7.
Derive an expression for critical pressure ratio of a nozzle. Explain the phenomenon of choking in the nozzle. 10 A steam power station uses the following cycle Steam boiler outlet 150 bar, 550°C 3450.4 kJ/kg, 6.523 kJ/kg Reheat at 40 bar to 550°C 3560'34 kJ/kg, S 7.235 kJ/kg Condenser at 0.1 bar (hf 191.8 kJ/kg, hfg 2392.05 kJ/kg, Sf 0·649 kJ/kg Sfg 7.5 kJ/kg Assuming ideal processes, find quality of steam at turbine exhaust, cycle efficiency and steam flow rate per kWh. 10

The air handling unit in an AC plant supplies a total of 4500 cmm of dry air which comprises by weight 20% fresh air at 40 DC DBT, 27 DC WBT and 80% recirculated air at 25 DC DBT and 50% RH. Air leaves the cooling coil at 13 DC saturated. Calculate total cooling load and room heat gain
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The following data refer to a 4-stroke, 4-cylinder diesel engine: Cylinder diameter =36 cm; Stroke =40 em; Speed =315 r.p.m.; Indicated MEP 7 bar; Brake power 250 kW; Fuel consumption 80 kg/hr; Calorific value 44 MJ/kg; Air consumption 30 kg/min; Cooling water circulated 90 kg/min with rise in temperature 38 DC; Exhaust gas temperature 324 DC and Room temperature 45 DC kJ/kg Cpair 1.005 kJ/kg Cp 1.05 kJ/kg Cp 2.093 kJ/kg K. In gas steam exhaust gases, partial pressure of steam is 0.03 bar and fuel contains 13% H2.
Find mechanical efficiency, indicated thermal Tb, brake specific fuel consumption: Draw heat balance sheet for the engine in hourly basis. 10

8. An R12 simple saturation cycle operates at temperatures of 35°C and
-15°C. Determine the COP and HP per ton of refrigeration of the system:
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Differentiate between summer and winter air-conditioning processes. 10
Even though velocity-compounded impulse turbines are less efficient, in the initial stages of high pressure turbines are normally velocity-compounded. Why? Plot the variation of pressure and velocities in velocity-compounded and pressure-compounded impulse turbines. 10
A steam power plant operates on ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa, 450 °C 3301.8 kJ/kg, 6.7193 kJ/kgK) and is condensed in the condenser at 20 kPa f 251.4 kJ/kg, hfg 2358.3 kJ/kg, vf 0.001 m3/kg, sf =0.832 kJ/kg Sfg =7.0766 kJ /kg K). Steam is extracted from the turbine at 0.4 MPa (hf 604.74 kJ/kg, vf 0-001 m3/kg, hfg 2133.8 kJ/kg, sf 1.7766 kJ/kg Sfg 5.1193 kJ/kg to heat feed water heater. Water leaves feed water heater as saturated liquid. Show the cycle on T-s diagram and find net work outputting of steam, the boiler and thermal efficiencies of the cycle. 20