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Q1. Air at 8.1bar, 0.024 m³ and 490 K with a mass of 0.138 kg of air is expanded isothermally to 5.2 bar.

The system is then further expanded polytropically to 2.8 bar and 416 K.

(a) Calculate EACH of the following:

(i) the polytropic index of expansion;

(ii) the net work;

(iii) the net heat;

(iv) the total change in entropy.

(b) Sketch the PV and TS diagrams.

Note: C_v, C_p and Rare 718 J/kgK, 1005 J/kgK and 287 J/kgK respectively.

Q2. In a Diesel cycle the polytropic compression ratio is 15 and the heat energy supplied at constant pressure is 1 MJ/kg.

The initial pressure and temperature of the air at the start of compression are 1 bar and 15°C respectively.

Calculate EACH of the following:

(a) the temperatures at all points;

(b) the cycle thermal efficiency.

Note: For compression: n = 1.35, for expansion: n = 1.25

C_v = 0.718 kJ/kgK and C_p = 1.005 kJ/kgK R = 0.287 kJ/kgK

Q3. A Single acting 3 stage reciprocating compressor is designed for minimum work with perfect intercooling. it deliver So. 11 kg/s of air from initial conditions of 1.10 bar and 15℃ and has a volume compression ratio of 2.41 for EACH stage according to the law pV^1.38 = C.

(a) Draw graph pV diagram showing intercooling.

(b) Calculate each of the following:

(i) each stage delivery pressure;

(ii) the total indicated power;

(iii) the total rate of heat removed in the intercoolers.

Note: C_v = 0.718kJ/kgK and C_p = 1.00SkJ/kgK

Q4. A steam turbine isentropically expands steam from a pressure 60 bar and superheated temperature of 415°C to· 6 bar. The feed water leaves the condenser with no undercooling, the feed pump work cannot be ignored.

a) Sketch the T-s diagram for the cycle. (2)

b) Calculate the thermal efficiency of the cycle. (14)

Q5. A vapour compression cycle using Tetrafluoroethene (R134a) has compressor suction and discharge of 3.4966 bar and 11.595 bar respectively.

The vapour enters the compressor in a dry saturated state and leaves at a temperature of 62°C. The liquid refrigerant has 5 K of subcooling at the entry to the expansion valve.

(a) Sketch Ph and Ts diagrams.

(b) Determine EACH of The following:

(i) the isentropic efficiency of the compressor.

(ii) the dryness factor entering the evaporator.

(iii) the coefficient of Performance.

Q6. A pipe of diameter 0.3 m carries a fluid, and EACH metre length generates 185 watts of heat. The surrounding air is at 6℃ and the surface heat transfer coefficient is 9 W/m²K.

a) Calculate the temperature of the pipe.

b) The pipe was covered in insulation 2cm thick and a thermal conductivity of 5W/mK. The outer heat transfer coefficient maybe assumed to remain the same.

Calculate the new temperature of the pipe.

Q7. A Natural gas consists of the following volumetric composition, Propane C₃H₈ (50%) and Ethene C₂H₄ (50%).

Determine EACH of the following:

(a) the Stoichiometric volume of air, for the complete combustion of 3.5 m³; (10)

(b) the percentage volumetric analysis of the exhaust gas products. (6)

Q8. An impulse turbine has a nozzle at entrance.

(a) Calculate the nozzle exit velocity if the change in enthalpy across the nozzle is 720 kJ/kg. (2)

(b) Sketch a blade velocity diagram labelling all significant angles and velocities. (3)

(c) The nozzle entrance angle is 14°, the blade velocity is 460 m/s, and the blades are symmetrical and have an angle of 38°.

Determine the diagram power if the blade velocity coefficient is 0.98 and the mass flowrate of the steam is 0.6 kg/s. (11)

Q9. A centrifugal pump impeller is 1.2 m outside diameter and 0.85 m inside diameter and runs at 720 rpm. The radial velocity at the inlet and the outlet is 27.2 m/s. The tangential component is 16.1 m/s, and the volumetric flow rate throughout is 0.5 m³/s.

Calculate EACH of the following:

(a) the blade outlet angle;

(b) the blade inlet angle;

(c) the width of the impeller at the inlet and outlet;

(d) the power.

Note: the density of water is 1000 kg/m³