Handouts
LINK: Steam Power Plants
Topics:
Simple Rankine Cycle
Irreversibilities and losses in a Rankine Cycle
Steam Turbine
Geothermal Power Plant
Variable Load Analysis
Exercises
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1. A 25 kg of water at 55oC saturated is vaporized until it is completely vaporized. Determine the volume of water vaporized in the tank, in m3. a. 139.2 b. 209.1 c. 189.9 d. 239.2 2. At 190oC the entropy of a substance is 5.5, what is the quality of the substance? a. 76.4% b. 67.3% c. 55.9% d. 49.7% 3. A 25 liter tank contains saturated liquid and saturated vapor at 250oC. If the mass of the liquid is 10 kg, determine the moisture content of steam. a. 67.0% b. 58.3% c. 97.57% d. 83.1% 4. Determine the approximate enthalpy of the feed water at 45oC? a. 108.3 b. 188.4 c. 209.3 d. 158.8 5. Determine the approximate enthalpy of water at 200oF. a. 183.9 b. 167.3 c. 251.8 d. 200.0 6. A 12 m3 container contains 6 m3 of liquid water and 6 m3 of saturated water vapor at 120 kPa. Find the internal energy of the system, in kJ, using steam tables. At 120 kPa: vf=1.0473x10-3 m3/kg; vg=1428.4x10-3 m3/kg, uf=439.20 kJ/kg; ug=2512.1 kJ/kg. a. 2.52 x 106 b. 3.66 x 106 c. 4.10 x 106 d. 5.91 x 106 7. Using steam tables, determine the average constant specific heat (Cp) of steam at 15 kPa and 50 deg C. At 50 deg C: h=2592.1 kJ/kg. At 53.97 deg C: h=2599.1 kJ/kg. a. 1.76 kJ/kg-K b. 2.37 kJ/kg-K c. 3.33 kJ/kg-K d. 1.09 kJ/kg-K 8. A vessel with a volume of 1.5 m3 contains liquid water and vapor in equilibrium at 620 kPa. The liquid water has a mass of 1.2 kg. Using steam tables, find the mass of water vapor, in kg. At 620 kPa: vf=1.1021x10-3 m3/kg; 306x10-3 m3/kg. a. 3.87 b. 4.89 c. 5.11 d. 6.07 9. Find the entropy of steam at 70.9 psia with a quality of 0.70. At 70.9 psia: sg=1.6288 Btu/lb-oR, sf=0.4417 Btu/lb-oR. a. 2.87 b. 2.07 c. 1.27 d. 1.59
10. One kilogram of water (Cv = 4.2 kJ/kg-K) is heated by 310 Btu of energy. Calculate the change in temperature, in K. a. 57.34 b. 77.87 c. 67.30 d. 88.11 11. A steam condenser in a Rankine cycle as an inlet condition of 160 kPa and 85% quality. If the mass of steam is 1.8 kg/s, determine the kilograms per minute of cooling water in the condenser for 15oC rise in temperature. At 160 kPa: hf=475.36 kJ/kg, hfg=2221.1, hg=2696.5 a. 34.09 b. 43.14 c. 59.91 d. 54.11 12. A Rankine cycle has an output of 6000 kW. The overall plant efficiency is 70% and if the factor of evaporation is 1.3, determine the mass of steam evaporated. a. 9831.2 kg/hr b. 11697.1 kg/hr c. 12001.2 kg/hr d. 10516.73 kg/hr 13. A Rankine cycle has a steam throttle condition of 5 MPa and 400oC. If the turbine exhaust is 100 kPa, using steam tables determine the cycle efficiency. a. 15% b. 16% c. 20% d. 25% 14. A Rankine cycle has a turbine work of 650 kJ/kg and an efficiency of 85%, the pump work is 4 kJ/kg and has an efficiency of 70%. If the cycle efficiency is 30%, calculate the heat added in the cycle, in kJ/kg. a. 2039.68 b. 1832.66 c. 2899.1 d. 2539.69 15. A Rankine cycle has an initial mass of liquid flowing at 18 kg at 80oC with an enthalpy of 1300 kJ/kg, find the change in enthalpy of the system, in kJ/kg. a. 901.3 b. 965.09 c. 981.3 d. 930.8 16. The available enthalpy of a turbine is 3500 kJ/kg in a Rankine cycle. If the pump work has 30 kJ/kg with a flow of 3.5 kg/s, determine the system output. a. 10153.1 kW b. 15013.1 kW c. 12145.0 kW d. 13110.2 kW 17. The available enthalpy of steam at the exit of a boiler in a Rankine cycle is 2920 kJ/kg and enthalpy at the turbine entrance of 2880 kJ/kg. If the mass of steam is 4.0 kg/s, determine the heat loss between the boiler exit and turbine entrance. a. 160 kW b. 155 kW c. 189 kW d. 143 kW 18. In a given Rankine cycle, steam enters the turbine at 4 MPa (entalphies and entropies given) and condenser of 55 kPa. (Properties given), what is the thermal efficiency of the cycle? At 4MPa: hg=2801.4 kJ/kg, sg=6.0701 kJ/kg-K. At 55 kPa: hf=350.54, hfg=2299.3, sf=1.1193, sfg=6.4422, vf=1.0316 x10-3 m3/kg a. 20.36% b. 25.01% c. 29.31% d. 27.71% 19. Steam flows into a turbine at a rate of 15 kg/s. and 15 kW of heat are lost from the turbine. Ignoring potential and kinetic energy effects, find the power output of the turbine. The inlet conditions are 2.5 MPa and 380oC (h=3194.4 kJ/kg) and 0.15 MPa and 100% quality (h=2693.6 kJ/kg). a. 6459 kW b. 7497 kW c. 8801 kW d. 5891 kW 20. The available enthalpy of a turbine is 1300 kJ/kg, the turbine efficiency is 80%, and full load capacity is 4500 kW. Determine the full load steam consumption in kg/kW-hr. a. 1.46 b. 3.46 c. 2.22 d. 4.07 21. A steam condenser receives 15 kg/s of steam with an enthalpy of 2690 kJ/kg. Steam condenses into a liquid and leaves with an enthalpy of 290 kJ/kg. Cooling water passes through the condenser with an increase of temperature from 15o to 30oC. Find the water flow rate, in kg/s. a. 503.11 b. 573.20 c. 612.3 d. 653.2 22. A heat exchanger was installed purposely to cool 0.90 kg of gas per second. Molecular weight is 30 and k=1.33. The gas is cooled from 160oC to 75oC. Water is available at a rate of 0.60 kg/s and at a temperature of 15oC. Calculate the exit temperature of water, in oC. a. 49 b. 47 c. 51 d. 46 23. A steam turbine with 85% stage efficiency receives steam at 6 MPa and 560oC and exhaust as 60 kPa. Find the turbine work, in kJ/kg. At 6MPa and 560 deg C: h=3564.2 kJ/kg, s=7.0573 kJ/kg-K. At 60 kPa: hf=359.86, hfg=2299.3, sf=1.1453, sfg=6.3867. a. 914.5 b. 801.5 c. 798.3 d. 645.3 24. A steam turbine 90% stage efficiency receives steam at 8 MPa and 580oC and exhaust at 25 kPa. Determine the actual exhaust enthalpy. At 8MPa and 580 deg C: h=3593.8 kJ/kg, s=6.9646 kJ/kg-K. At 25 kPa: hf=271.93, hfg=2346.3, sf=0.8931, sfg=6.9383. a. 2003.87 b. 3687.3 c. 2583.1 d. 2451.9 25. A steam turbine with 7 MW capacity has a Willian’s line equation of ms=6.3L + 3100 kg/hr. Find the steam consumption at 75% load, in kg/hr. a. 39871 b. 2871.3 d. 38817.0 26. Steam in a Rankine cycle is expanded from 210 psia saturated vapor state to 20 psia. The turbine has an efficiency of 82%. What is the actual enthalpy after expansion? Properties: At 210 psi: hg=1202.4558 Btu/lb, sg=1.4361 Btu/lb-oR. At 20 psi: hf=196.2 Btu/lb, hfg=960.2 Btu/lb, sf=0.2259 Btu/lb-oR, sfg=1.3969 Btu/lb-oR. a. 873.2 b. 973.1 c. 997.5 d. 801.3 27. A liquid dominated geothermal power plant with a single flash separator receives water at 200 deg C. The separator pressure is 1.0 MPa. A direct contact condenser operates at 0.044 MPa. For a cycle output of 50 MW, determine the mass flow rate of the well-water, in kg/s. At 200 deg C: hf=858.45 kJ/kg a. 1851.5 b. 1601.2 c. 1567.3 d. 2079.5 28. Ground water in a geothermal power plant has a ground water flow of 48 kg/s. If the quality of hot water entering the flash tank is 14%, determine the mass of steam entering the turbine, in kg/s. a. 6.72 b. 8.32 c. 4.22 d. 7.87 29. In a 15 MW geothermal power plant, the mass of steam entering the turbine is 30 kg/s. The quality after throttling is 25% and enthalpy of ground water is 750 kJ/kg. Find the overall efficiency of the plant. a. 14.38% c. 18.21% d. 22.38% 30. The power duration curve for a hydro-electric power installation shows 870 x 105 kW-hr of electrical energy can be obtained during the year. The plant has an annual load factor of 30%. If the plant capacity factor is 25%, find the capacity of the power station and the reserve capacity of the plant, respectively. a. 389,381.3 kW, 52,812.9 kW |
