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Q1. A mass of 1 kg of argon at a pressure and temperature of 20 bar and 127℃ respectively, expands in an isentropic process to a pressure of 2 bar.

It is then compressed to the original pressure according to the law PV_n = constant. The overall decrease in entropy is 0.217 kJ/K.

(a) Sketch the processes on Pressure-Volume and Temperature-specific entropy diagrams. (2)

(b) Calculate EACH of the following:

(i) The temperature at the end of compression; (3)

(ii) The polytropic index of compression; (4)

(iii) The net work transfer;(4)

(iv) The net heat transfer. (3)

Note: For Argon γ = 1.67 , C_P = 520.3  J⁄(kg K)

Q2. An open cycle gas turbine plant with a regenerator is shown in Fig Q2. The air enters the compressor at a pressure and temperature of 1 bar and 17℃ respectively. It is then compressed with an isentropic efficiency of 0.82 to a pressure of 6 bar. The combustion gas enters the turbine at a temperature of 827℃ and is expanded with an isentropic efficiency of 0.88 to a pressure of 1 bar.

The regenerator is fitted with a bypass and may be considered as a perfect heat exchanger. The mass flow of fuel and other system losses may be ignored.

(a) Calculate EACH of the following:

(i) The specific net-work output; (6)

(ii) The decrease in thermal efficiency when the regenerator is fully bypassed. (6)

(b) Sketch the cycle on a Temperature-specific entropy diagram showing the effect of the regenerator. (4)

Note: For air γ = 1.4, C_P = 1.005  kJ⁄(kg K)

For gas γ = 1.33, C_P = 1.15  kJ⁄(kg K)

Q4. The shell of a steam condenser has a volume of 10 m³ and contains dry saturated steam and air. At a particular instant the vacuum gauge reads 660 mm of mercury and the internal temperature is 38℃ .

After a period of time the temperature has fallen to 26.7℃ and the vacuum gauge reads 560 mm of mercury. The atmospheric pressure remains constant 1014 mbar.

Calculate EACH of the following:

(a) The initial mass of air present;(5)

(b) The initial mass of dry saturated vapour;(2)

(c) The mass of air that has leaked into the condenser;(5)

(d) The mass of vapour condensed. (4)

Note: For mercury ρ = 13600  kg⁄m³

For air R = 287 J/kg K.

Q5. Steam flows through one stage of a pressure compounded impulse turbine at the rate of 1.5 tonne/hour. The steam enters the nozzle with a velocity of 170 m/s and a pressure of 30 bar, 400℃ respectively

The nozzles are set at 20° to the plane of rotation and expand the steam with an isentropic efficiency of 95% to a pressure of 15 bar. The blades have an exit angle 10° less than their inlet angle and a velocity coefficient of 0.9.

(a) Calculate the absolute velocity of the steam leaving the nozzles. (4)

(b) Draw the stage velocity vector diagrams to a scale of 1 mm = 5 m/s.(6)

(c) Determine EACH of the following for the stage:

(i) The diagram power; (2)

(ii) The axial thrust; (2)

(iii) The diagram efficiency. (2)

Note: Blade speed ratio =   cos⁡α_i/2

Q6. A vapour compression refrigeration plant is used to produce ice at  from fresh water at .

The R134a refrigerant is compressed in an isentropic process from suction conditions of 1.3272 bar,  to discharge pressure of 10.163 bar.

The temperature rise of the condenser fresh water cooling is 10 K at a flow rate of 22 tonne/hour. The refrigerant enters the expansion valve at a temperature of

(a) Sketch the cycle on Pressure-specific enthalpy and Temperature-specific entropy diagrams. (2)

(b) Calculate EACH of the following:

(i) The compressor discharge temperature;(4)

(ii) The mass flow rate of refrigerant required;(5)

(iii) The rate of ice production in tonne per hour. (5)

Note: for fresh water C = 4.2 kJ/kg K

For ice C = 2.1 kJ/kg K, enthalpy of fusion = 335 kJ/kg.

Q7. A furnace wall is made from 10 mm thick steel plate lined internally with refractory 100 mm thick. The external surface is a sheet steel casing, creating a 200 mm wide air gap. A 40 % reduction in heat loss is to be achieved by insulating the external side of the furnace wall, while the position of the steel casing remains unchanged.

The internal surface temperature of the refractory is 1800℃ and the temperature of the surroundings remains constant at 25℃.

The effect of the sheet steel casing may be ignored.

(a) Calculate EACH of the following:

(i) The rate of heat loss per m² without insulation; (4)

(ii) The required thickness of insulation;(5)

(iii) The temperature drop across the final air gap. (4)

(b) Sketch the thermal gradient across the insulated wall showing the interface temperature. (3)

Note: thermal conductivity of the refractory = 0.31 W/mK

thermal conductivity of steel = 55 W/mK

thermal conductivity of air = 0.04 W/mK

thermal conductivity of insulation = 0.023 W/mK

outer surface heat transfer coefficient = 11 W/m²K

Q8. A two-stage single acting reciprocating air compressor is designed for minimum work and perfect intercooling. The inlet pressure and temperature are 0.9 bar and 25℃ respectively, the delivery pressure is 32.4 bar.

The free air capacity of the compressor is 8.5 m³/min at a speed of 360 rev/min and a pressure and temperature of 1.013 bar and 0℃ respectively. The clearance ratio of each stage is 0.05 and polytropic index for all compression and expansion processes is 1.28.

(a) Sketch the cycle on a Pressure -Volume diagram indicating the work saved by intercooling. (3)

(b) Calculate EACH of the following:

(i) The total volume of the low-pressure cylinder; (5)

(ii) The indicated power of the machine; (3)

(iii) The power saved by intercooling.(5)

Q9. A rectangular plate has a mass of 5.45 kg and is suspended vertically by a hinge on the top horizontal edge. The centre of gravity of plate is located 10 cm below the hinge.

A horizontal jet of fresh water 25 mm in diameter and flowing with a velocity of 5.65 m/s strikes the plate 15 cm below the hinge.

At this condition the plate is held in the vertical position by a compressed spring acting at its centre of gravity.

The flow rate of the jet is increased, and the plate is deflected to an angle of 30° to the vertical against the spring force which remains constant.

Friction in the hinge may be ignored.

(a) Calculate EACH of the following.

(i) The spring force holding the plate vertical; (4)

(ii) The increase in the jet velocity to deflect the plate. (8)

(b) Sketch the force diagram for the condition given in Q9 (a)(ii). (4)