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Q1. Air at a pressure and temperature of 5.5 bar and 1300 K respectively is cooled at constant volume until the pressure is 1.35 bar.

The air is the n reversibly compressed according to the law pV^1.28 = constant, back to the original pressure.

(a) Sketch The sequence of process on pressure- Volume and Temperature -specific entropy diagrams. (2)

(b) Calculate EACH of the following for 1 kg of air:

(i) The work transfer; (4)

(ii) The total change in internal energy; (3)

(iii) The net heat transfer; (4)

(iv) The overall change in entropy. (3)

Note: for air R = 0.287 kJ/kg K and C_v = 0.718 kJ/kg K.

Q2. In an air standard dual combustion cycle the volume compression ratio is 20 : 1

The minimum pressure and temperature are 2.0 bar and 47℃ respectively.

The maximum pressure is 200 bar and the maximum temperature is 1685℃.

(a) Sketch the cycle on pressure-Volume and Temperature-specific entropy diagrams. (3)

(b) Calculate EACH of the following:

(i) The pressure and temperature at each point in the cycle; (5)

(ii) The percentage of the total heat added at constant volume; (5)

(iii) The cycle Thermal efficiency. (3)

Note: for air γ = 1.4 and R = 0.287  kJ⁄(kg K).

Q3. A pure hydrocarbon fuel is burned in air. The mass analysis of the dry combustion is 5.13 kg of CO₂, 1 kg CO, 1.8 kg O₂, 25.23 kg N₂. Calculate EACH of the following:

(a) the mass analysis of the fuel; (8)

(b) the percentage excess air by mass; (4)

(c) the molecular mass of total combustion products. (4)

Note: atomic mass relationships H = 1, C = 12, O = 16, N = 14. air contains 23.3% oxygen by mass.

Q4. Steam at a pressure of 20 bar and a specific volume of 0.1511 m³/kg enters a convergent divergent nozzle with a negligible velocity.

The steam expands isentropically according to taw pV^1.3 = constant into a space at a pressure of 3 bar.

The diameter of the throat is 10 mm and the specific enthalpy drop in the divergent section is 295.5 kJ/kg.

Calculate EACH of the following:

(a) the critical pressure; (2)

(b) the specific volume of the steam at the throat; (3)

(c) the mass flow rate of steam; (5)

(d) the diameter of the nozzle at exit. (6)

Note: For the nozzle p_c = p_o (2/(n+1))^n/n-1 ; C_c  = (np_c V_c )^1/2

Q5. Steam at a pressure and temperature of 4 bar and 200℃ respectively, leaves the fixed blades of a 50 % reaction turbine stage.

The moving blade inlet and outlet angles are 50° and 35° respectively. The mean blade speed is 170 m/s. The blade height is 10 % of the blade ring mean diameter. The mass flow rate of steam through the stage is 14 kg/s.

Calculate EACH of the following:

(a) The blade height; (5)

(b) The stage power; (4)

(c) The percentage increase in the moving blade relative velocity; (4)

(d) The stage specific enthalpy drop. (3)

Q6. A vapour compression refrigeration plant uses R134a and operates between pressures 1.0637 bar and 10.163 bar. The refrigerant enters the compressor at a temperature of -25℃ and leaves at a temperature of 55℃. The refrigerant leaves the condenser with 10 K subcooling. At These conditions the power input to the plant is 117 kW with a mechanical efficiency of 90 %.

(a) Sketch The cycle on pressure-specific enthalpy and Temperature-specific entropy diagrams. (4)

(b) Calculate EACH of the following:

(i) The isentropic efficiency of the compressor; (6)

(ii) The cooling load; (4)

(iii) The plant coefficient of performance. (2)

Q7. An air- cooled heat exchanger has 9 tubes each of 40 mm mean diameter in a single pass, parallel flow arrangement.

Fresh water flows through the tubes with a velocity of 0.2 m/s. It enters at a temperature of 85℃ and leaves at a temperature of 75℃. The air enters the cooler at a temperature of 4℃ and has a mass flow of 9 kg/s.

(a) Calculate EACH of the following.

(i) The rate of heat transfer from the water; (3)

(ii) The log means temperature difference for the cooler; (5)

(iii) The length of EACH cooler tube. (5)

(b) Sketch the cooler temperature distribution (profile) diagram (3)

Note: for air c_p =1.005  kJ⁄(kg K)

for water c = 4.2  kJ⁄(kg K)

heat transfer coefficient for air side of the tube = 8.84  kW⁄(m² K)

heat transfer coefficient for water side of the tube = 13.74  kW⁄(m² K).

Q8.A single acting, three stage reciprocating compressors, is designed for minimum work with perfect intercooling. It delivers 8 kg/mi of air from initial conditions of 1.15 bar and 25℃ and has a volumetric efficiency of 0.88 at a speed of 360 rev/min.

The clearance volume in each stage is 5 % of the respective swept volume.

Compression and expansion pressures take place according to the law pV^1.25 = constant.

(a) Calculate EACH of the following:

(i) The stage delivery pressure; (5)

(ii) The indicated power; (3)

(iii) The total heat removed in the intercoolers. (4)

(b) Sketch the cycle on a pressure- Volume diagram, indicating the stage pressures. (4)

Note :for air R = 287 J⁄(kg K)  ,C_p= 1005  J⁄(kg K)

Q9.A reducing bend is fitted in a horizontal section of freshwater system as shown in Fig Q9. It turns the flow through an angle of 90^o anticlockwise to the direction of flow.

The system pressure and fluid velocity at inlet are 8 bar and 1.5 m/s respectively.

The bend has diameters of 300 mm at inlet and 150 mm at outlet.

The friction loss in the bend may be ignored.

Calculate EACH of the following:

(a) The system pressure at the bend outlet; (4)

(b) The forces acting in the X and Y directions due to the charge in diameter; (3)

(c) The forces acting in X and Y directions due to the change in momentum; (3)

(d) The magnitude of the resultant force acting on the bend; (4)

(e) The direction of the resultant force. (2)