Problems on Thermodynamics part2

Problems:

1. 12 kg of a fluid per minute goes through a reversible steady flow process. The properties of fluid at the inlet are p1 = 1.4 bar, r1 = 25 kg/m3, V1 = 120 m/s & u1 = 920 kJ/kg and at the exit are p2 = 5.6 bar, r2 = 5 kg/m3, V2 = 180 m/s and u2 = 720 kJ/kg. During the passage, the fluid rejects 60 kJ/s and raises through 60m. Determine i) the change in enthalpy ii) work done during the process.

Negative sign indicates work is done on the fluid in the reversible steady flow process.

2. In the turbine of a gas turbine unit the gases flow through the turbine at 17 kg/s and the power developed by the turbine is 14000 kW. The enthalpies of the gases at inlet and outlet are 1200 kJ/kg and 360 kJ/kg respectively, and the velocities of the gases at inlet and outlet are 60 m/s and 150 m/s respectively. Calculate the rate at which the heat is rejected from the turbine. Find also the area of the inlet pipe given that the specific volume of the gases at inlet is 0.5 m3/kg.

3. Air flows steadily at the rate of 0.4 kg/s through an air compressor entering at 6 m/s with a pressure of 1 bar and a specific volume of 0.85 m3/kg, and leaving at 4.5 m/s with a pressure of 6.9 bar and a specific volume of a 0.16 m3/kg. The internal energy of air leaving is 88 kJ/kg greater than that of the air entering. Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 59 kJ/s. Calculate the power required to drive the compressor and the inlet and outlet pipe cross sectional areas.

4. A turbine operating under steady flow conditions receives steam at the following state. pressure 13.8 bar, specific volume 0.143 m3/kg, i.e., 2590 kJ/kg, velocity 30 m/s. The state of the steam leaving the turbine is pressure 0.35 bar, specific volume 4.37 m3/kg, i.e., 2360 kJ/kg, velocity 90 m/s. Heat is lost to the surroundings at the rate of 0.25 kJ/s. If the rate of steam flow is 0.38 kg/s, what is the power developed by the turbine? (102.8 kW).

5. At the inlet to a certain nozzle the enthalpy of the fluid is 3025 kJ/kg and the velocity is 60 m/s. At the exit from the nozzle the enthalpy is 2790 kJ/kg. The nozzle is horizontal and there is negligible heat loss from it. i) Find the velocity at the nozzle exit. ii) If the inlet area is 0.1 m2 and specific volume at inlet is 0.19 m3/kg, find the rate of flow of fluid. iii) If the specific volume at the nozzle exit is 0.5 m3/kg, find the exit area of the nozzle.

6. In a steam power plant 1.5 kg of water is supplied per second to the boiler. The enthalpy and velocity of water entering the boiler are 800 kJ/kg and 10 m/s. Heat at the rate of 2200 kJ/kg of water is supplied to the water. The steam after passing through the turbine comes out with a velocity of 50 m/s and enthalpy of 2520kJ/kg. The boiler inlet is 5m above the turbine exit. The heat loss from the boiler is 1800 kJ/m and from the turbine 600 kJ/min. Determine the power capacity of the turbine, considering boiler and turbine as single unit.

7. A centrifugal air compressor used in gas turbine receives air at 100 KPa and 300 K and it discharges air at 400 KPa and 500 K. The velocity of air leaving the compressor is 100 m/s. Neglecting the velocity at the entry of the compressor, determine the power required to drive the compressor if the mass flow rate is 15 kg/sec. Take Cp(air) = 1 kJ/kgK, and assume that there is no heat transfer from the compressor to the surroundings.

8. In a water cooled compressor 0.5 kg of air is compressed/sec. A shaft input of 60 kW is required to run the compressor. Heat lost to the cooling water is 30% of input and 10% of the input is lost in bearings and other frictional effects. Air enters the compressor at 1 bar and 200C. Neglecting the changes in KE & PE, determine the exit air temperature. Take Cp = 1kJ/kg0C air.

9. A petrol engine develops 50 kW brake power. The fuel and air flow rates are 10 kg and 107 kg/hr. The temperature of fuel air mixture entering the engine is 200C and temperature of gases leaving the engine is 5000C. The heat transfer rate from the engine to the cooling water circulated is 50kJ/s and that to the surroundings 10 kJ/s. Evaluate the increase in the specific enthalpy of the mixture as it flows through the engine.

10. Air at a temperature of 150C passes through a heat exchanger at a velocity of 30 m/s where its temperature is raised to 8000C. It then enters a turbine with the same velocity of 30 m/s and expands until the temperature falls to 6500C. On leaving the turbine, the air is taken at a velocity of 60 m/s to a nozzle where it expands until the temperature has fallen to 5000C. If the air flow rate is 2 kg/s, calculate i) the rate of heat transfer to the air, ii) the power output from the turbine assuming no heat loss, and iii) the velocity at exit from the nozzle, assuming no heat loss. Take the enthalpy of air as h = Cpt, where Cp = 1.005 kJ/kg0C.

11. A 260 mm dia cylinder fitted with a frictionless leak pro of piston contains 0.02 kg of steam at a pressure of 6 x 105 N/m2 and a temperature of 2000C. As the piston moves slowly outwards through a distance of 305 mm the steam undergoes a fully resisted expansion according to the law pVn = a constant to a final pressure 1 x 105N/m2. Determine i) value of the index n ii) work done by the steam iii) Magnitude and sign of heat transfer.

12. Air flows steadily at the rate of 0.5 kg/s through an air compressor, entering at 7 m/s velocity, 100 KPa pressure, 0.95 m3/kg volume, and leaving at 5 m/s velocity, 700 KPa pressure and 0.19 m3/kg. The internal energy of the air leaving is 93 kJ/kg greater than that of the air entering. Cooling water in the compressor jackets absorbs heat from the air at the rate of 58 kW. i) compute the rate of shaft work in kW ii) find the ratio of the inlet pipe dia to outlet pipe diameter.

13. A gas flows into a turbine with an initial pressure of 7 bar, specific volume 0.2 m3 and velocity 150 m/s. The corresponding values of pressure, specific volume and velocity at the exit are 3.5 bar, 0.5 m3 and 300 m/s respectively. During the expansion of gas in the turbine its internal energy decreases by 92 kJ/kg and loss due to radiation was 13 kJ/kg. What amount of shaft work is developed per kg of gas flow.

14. The compressor of a large gas turbine receives air from the surroundings at 95 KPa and 200C. The air is compressed to 800 KPa according to the relation pV1.3 = constant. The inlet velocity is negligible and the outlet velocity is 100 m/s. The power input to the compressor is 2500 kW, 20% of which is removed as heat from the compressor. What is the mass flow rate of the air? Take Cp = 1.01 kJ/kg0K for air.

15. The steam supply to an engine is comprised of two streams which mix before entering the engine. One stream is supplied at the rate of 0.01 kg/s with an enthalpy of 2950 kJ/kg and a velocity of 20 m/s. The other stream is supplied at the rate of 0.1 kg/s with an enthalpy of 2569 kJ/kg and a velocity of 120 m/s. At the exit from the engine the fluid leaves as two streams, one of water at the rate of 0.001 kg/s with an enthalpy of 420 kJ/kg and the other of steam. The fluid velocity at the exit are negligible. The engine develops a shaft power of 25 kW. The heat transfer is negligible. Evaluate the enthalpy of the second exit stream. (Ans. 2462 kJ/kg)

16. A perfect gas flows through a nozzle where it expands in a reversible adiabatic manner. The inlet conditions are 22 bar, 5000C, 38 m/s. At exit the pressure is 2 bar. Determine the exit velocity and exit area if the flow rate is 4 kg/s. Take R = 190 J/kg-0k and g = 1.35

17. A steam turbine operate under steady flow conditions receiving steam at the following state: Pressure 15 bar, internal energy 2700 kJ/kg, velocity 300 m/s, specific volume 0.17 m3/kg and velocity 100 m/s.

The exhaust of steam from the turbine is at 0.1 bar with internal energy 2175 kJ/kg, specific volume 15m3/kg and velocity 300 m/s. The intake is 3 m above the exhaust. The turbine develops 35 kW and heat loss over the surface of turbine is 20kJ/kg. Determine the steam flow rate through the turbine. [Ans.: 0.0614 kg/s]

18. Determine the power required to drive a pump which raises the water pressure from 1 bar at entry to 25 bar at exit and delivers 2000 kg/hr of water. Neglect changes in volume, elevation and velocity and assume specific volume of water to be 0.001045m3/kg.

19. In a conference hall comfortable temperature conditions are maintained in winter by circulating hot water through a piping system. The water enters the piping system at 3 bar pressure and 500C temperature (enthalpy = 240 kJ/kg) and leaves at 2.5 bar pressure and 300C temperature (enthalpy = 195 kJ/kg). The exit from the piping system is 15 m above the entry. If 30 MJ/hr of heat needs to be supplied to the hall, make calculation for the quantity of water circulated through the pipe per minute. Assume that there are no pumps in the system and that the change in KE is negligible.