Thermo Numericals

Steady-Flow Equation

1. In a gas turbine power plant, gases flow through turbine at 17kg/s and power developed by the turbine is 1400,0000W. Specific enthalpies at inlet and outlet is 1200kJ/kg and 360kJ/kg respectively. Velocity at inlet and outlet is 60m/s and 150m/s respectively. Find heat flow rate (Q dot) and area of inlet pipe (A1). Specific volume of gases at inlet is 0.5m3/kg. Take z1=z2=0.
(Q dot = -119.35kW, A1=0.141m3)


2. Air flows at steady state of 0.4 kg/s through an air compressor entering at 6m/s with a pressure of 1 bar and specific volume of 0.85m3/kg and leaving at 4.5m/s with a pressure of 6.9 bar and specific volume of 0.16m3/kg. The change in specific energy is 88kJ/kg. Heat absorbed by cooling water is 59kW (taken out). Calculate power required by the input of the compressor and areas of outlets and take z1=z2.

3. Steady flow steam enters the condenser with h1=2300kJ/kg and c1=350m/s and leaves it with h2=160kJ/hg and c2=70m/s. Find Q dot. Remember W dot = 0 for condenser.
(Use the formula (h1+c12/2)+(Q dot/m dot) = (h2+c22/2)

4. A fluid undergoes a steady adiabatic flow through nozzle (W=0), such that h1=3025 kJ/kg, h2=2790 kJ/kg and c1=60m/s. Calculate velocity of the fluid at exit (c2), mass flow rate (m dot) when A1=0.1m2 and v1=0.1m3/kg and nozzle exit area if v2=0.5 m3/kg.
(c2= 688m/s, m dot= 31.6kg/s and A2=0.0229m2)

5. Unit mass flow rate expanding in turbine develops 12,000kW entering at 70m/s with a specific volume of 1m3/kg and leaving at a pressure of 3.5 bar ans specific volume of 0.85m3/kg. The exit area is 0.02m2 and heat rejected to cooling water is 61kW. Calculate pressure required to push the fluid in turbine, if change in specific internal energy is 55kJ/kg.
(P1 = 0.124 bar)

6. Unit mass of gas at initial pressure of 28 bar and with an internal energy of 1500kJ is contained in a well insulated cylinder of volume 0.06m3. The gas is allowed to expand behind a piston until its internal energy is 1400kJ. The law of expansion is PV^2=C. Calculate work done, final volume and final pressure.
(W = -100kJ, V2=0.044, P2=52 bar)


Steam Tables

7. Calculate dryness fraction, specific volume and specific internal energy of steam at 7 bar, where specific enthalpy is 2600kJ/kg.
(x = 0.921, v=0.2515m3/kg, u=2420kJ/kg)

8. Steam at a pressure of 110 bar and v=0.0196m3/kg. What is T (temperature), h (enthalpy) and u (internal energy)?
(T = 350 degree celsius, h=2889kJ/kg, u=2673 kJ/kg)

9. Given that P=150 bar, h=3309kJ/kg, find T, v and u?
(T=500 degree celsius, v=0.02078, u=2997kJ/kg)

10. Steam at 7 bar and dryness fraction 0.9 expands in a cylinder isothermally to a pressure of 1.5 bar. Calculate change in internal energy, change in enthalpy, when heat supplied during the process is 547kJ/kg. Also find work done/kg of steam.
(W = 217.5J/kg, Delta(u) = 216kJ/kg, Delta(h)=245.7)

11. 0.05kg of superheated steam is contained in a cylinder of 0.0076m3 volume. What is the temperature of the steam, if the vessel is cooled. At what temperature will the steam be just dry saturated. Cooling is continued until the pressure in vessel is 11 bar. Calculate final dryness fraction of steam and heat rejected in initial and final states.


T-S Diagram

12. Air at 15 degree celsius and 1.05 bar pressure occupies a volume of 0.02m3. The air is heated at constant volume, until the pressure is 4.2bar and then cooled at constant pressure, back to original temperature. Calculate net heat flow adn net entropy change.
(Q = -6.29kJ, S1-S3=0.01kJ/kg)



(Problems from first three lectures may be added later)