VARIABLE LOADS1. A Diesel power plant has a maximum demand of 120 MW with a load factor of 0.80 and capacity of 0.6. Estimate the plant capacity.A. 100 MWB. 160 MWC. 180 MWD. 200 MWSolution:

2. Calculate the MW power capacity of a Geothermal plant with a load factor of 0.82 and 120 MW peak load. The operation is limited to 8500 hours a year with a use factor of 0.70.A. 175B. 199C. 233D. 145Solution:

3. A given equipment consumes 5000 kw-hr/month at 24% rated plant capacity. It operates at 24 hours, 30 days/month. What is the rated capacity?A. 17.50 kwB. 23.90 kwC. 28.90 kwD. 82.94 kwSolution:

4. A central station is supplying energy to a community through two substations. One substation feeds four distribution circuits; the other, six. The maximum daily recorded demandsare:Power station12,000 kwSubstation A6,000 kwFeeder 11700Feeder 21800Feeder 32800Feeder 4600Substation B9,000 kwFeeder 1620Feeder 21500Feeder 31000Feeder 42900Feeder 52200Feeder 63000Calculate the diversity factor among feeders in substation B.A. 1.05B. 1.25C. 1.15D. 1.35Solution: Diversity factors among feeders in Substation B

5. The annual peak load on a 15,000-kw power plant is 10,500 kW. Two substations are being supplied by this plant. Annual energy dispatched through substation A is 27,500,000 kW-hr with a peak at 8,900 kw, while 16,500,000 kW-hr are being sent through substation B with a peak at 6,650 kw. Neglecting line losses, find the capacity factor of the power plant.A. 0.353B. 0.533C. 0.335D. 0.535Solution:

6. A power plant is said to have had a use factor of 48.5% and a capacity factor of 42.4%. How many hours did it operate during the year?A. 7660B. 8760C. 8920D. 10,020Solution:

Therefore

7. A distribution transformer supplies a group of general power customers having a connected load of 186 kw. If energy sells at 3.5 cents per kW-hr, what will be the monthly income from energy delivered through this transformer having an average motor efficiency of 75%.General data:Demand factor 0.75Diversity Factor 1.50Load factor0.45A. P1,047.00B. P1,074.00C. P1,407.00D. P1,470.00Solution: Actual maximum demand = demand factor x connected load Actual maximum demand = 0.75 x 186 = 139.5 kwSimultaneous maximum demand = sum of individual maximum demands / diversity factorSimultaneous maximum demand = 139.5 / 1.5 = 93 kwWith 75% motor efficiencySimultaneous maximum demand = 93 / 0.75 = 124 kwAverage load on transformer = load factor x peak loadAverage load on transformer = 0.45 x 124 = 55.8 kwKw-hrs delivered monthly = (55.8 kw)(30 days/mo.)(24 hrs/day)Kw-hrs delivered monthly = 40,176 kw-hrs/mo.Monthly income from energy delivered = (0.035/kw-hr)(40,176 kw-hr/mo.)Monthly income from energy delivered = P1,406.16 8. A daily load curve which exhibited a 15-minute peak of 6,520 kW is drawn to scales of 1 cm = 2 hrs and 1 cm = 500 kw. The area under the curve is measured by a planimeter and found to be 48.72 cm2. Determine the load factor based on the 15-minute peak.A. 0.211B. 0.411C. 0.311D. 0.511Solution: 1 cm2 = 500(2) = 1000 kw-hrsAverage load = (48.72 cm2)(1000 kw-hrs/cm2)( 1 day/24 hours)Average load = 2030 kwLoad factor = Average load / Peak loadLoad factor = 2030 / 6520Load factor = 0.311 9. A unit is rated at 80,000 kW. It operates for 6950 hrs during the year and generates 350,000,000 kW-hr. With a peak load of 75,500 kW, calculate the capacity factor.A. 50%B. 53%C. 79%D. 65%Solution:

10. A 25,000 kW plant has a utilization factor of 71% and a load factor of 39.6%. What is the average load on the plant in kW?A. 24,850B. 13,860C. 9,841D. 19,521Solution:Average load = (0.396)(25,000 kW) = 9,900 kW11. A steam cycle produces 40 MW of power, 50 MW of process heat and rejects 60 MW of heat. What is the utilization factor for this cycle?A. 50%B. 60%C. 70%D. 80%Solution:

Utilization Factor = 12. For a certain power plant, the load factor is 48%. The plant capacity is 42 MW. If the reserve over peak is 5 MW and the number of hours the plant not in service per year is 420, calculate the plant capacity factor.A. 0.324B. 0.387C. 0.423D. 0.46Solution:

13. The reserve over and above the peak load of a power station is 20 MW. For an annual factors as follows: load, 75% and capacity, 60%; determine the rated capacity of the power plant.A. 60 MWB. 75 MWC. 100 MWD. 44.44 MWSolution:(Load Factor)(Peak Load) = (Capacity Factor)(Rated Capacity) = Average Load(0.75)(Peak Load) = (0.60)(Rated Capacity)Rated Capacity Peak Load = 20 MW = Reserve(0.75)(Rated Capacity 20) = (0.60)(Rated Capacity)Rated Capacity = 100 MW14. A power plant is to have had a use factor of 46.5% and a capacity factor of 40.5%. Determine the number of hours did the plant operated during the year.A. 7269B. 7962C. 7629D. 7692Solution:

Equate :

FUELS AND COMBUSTION15. Find the air fuel ratio, in kg air per kg of fuel, for a combustion process to which the fuel is C8H20 with 20% excess air.A. 15.7B. 18.5C. 19.7D. 20.5Solution:

Solving for a, b and c

16. A fuel gas has the following volumetric analysis:CH4 = 68%C2H6 = 32%Assume complete combustion with 30% excess air at 101.325 kPa, 21 C wet bulb and 27 C dry bulb. What is the partial pressure of the water vapor in kPa?A. 8.62B. 19.28C. 16.94D. 14.24Solution:Theoretical Air

With 30% Excess air

Total moles in products = 1.32 + 2.32 + 0.3(2.48) + +1.3(2.48)(3.76) Total moles in products = 16.506Partial pressure = (2.32 / 16.506)(101.325) = 14.24 kPa

17. A diesel electric plant supplies energy for MECO. During a 240hr period, the plant consumed 300 gallons of fuel at 28 C and produced 4900 kw-hr. Industrial fuel used is 32 API and was purchased at P32.0 per liter at 15.6 C. What should the cost of fuel to produce one kw-hr?A. P7.05B. P7.35C. P7.69D. P6.00Solution: Computing for price per kg from per liter at 15.6 C

Density at 15.6 C = 0.8654 (1 kg/L) = 0.8654 kg/LPrice per kg = P32 / 0.8654 =P 36.977 per kg

Converting 300 gal per kw-hr to kg per kw-hr at 28 C

Cost per kw-hr = 0.1988 x P 36.977 = P7.35 per kw-hr

18. Calculate the mass of the combustion products of a diesel fuel oil (C16H30) with 30% excess air if the mass of fuel is 30 kg.A. 18.97 kgB. 169.1 kgC. 599.1 kgD. 569.1 kgSolution:

Solving for a, b and c

mf = 30 kgMass of product of combustion= (1 + Wta)mf = (1+18.889)(30) = 596.67 kg 19. A mixture of 101 kPa and 23 C that is 30% by weight CO2 and 70% by weight N2, determine the partial pressure of CO2.A. 3.182 kPaB. 21.65 kPaC. 100 kPaD. 25 kPaSolution:

For 100 kg of gas mixture:MassMolCO2 = 30 kg30/44 = 0.682 molN2 = 70 kg70/28 = 2.5 mol

nT = 0.682 + 2.5 = 3.182 mol

20. Find the air fuel ratio, in kg air per kg fuel, for a combustion process to which the fuel is C8H20 with 30% excess air.A. 3.76B. 10C. 13D. 20Solution:

Solving for a, b and c

21. At 28 API specific gravity, what is the heating value of oil in kJ/kg?A. 46,790B. 47,130C. 45,039D. 48,390Solution:

22. Dodecane (C12H26) is burned at constant pressure with 140% excess air. Determine the number of moles of oxygen in the products of combustion?A. 22.9B. 25.9C. 44.5D. 55.5Solution: Theoretical Air

With 140% Excess air

Mols of O2 = 1.4 x 18.5 = 25.9 mols 23. A mixture of 14.7 psia and 68 F that is 30% by weight CO2 and 70% by weight N2 has a partial pressure of CO2 in psia that is nearest to:A. 2.14B. 8.83C. 7.88D. 3.15Solution:

For 100 kg of gas mixture:MassMolCO2 = 30 lb30/44 = 0.682 molN2 = 70 lb70/28 = 2.5 mol

nT = 0.682 + 2.5 = 3.182 mol

24. Given gaseous fuel C8H18 and the volumetric products of combustion:CO2 = 10.01%, CO = 0.85%, N2 = 85%, O2 = 14%. Determine the air-fuel ratio.A. 18.0B. 20.1C. 15.0D. 24.0Solution:

Carbon Balance:8a = 10.01 + 0.85, a = 1.3575Nitrogen Balance:2(b)(3.76) = 2(85), b = 22.606No need to determine c.

(b)25. A manufacturing company in Bicol operates a Diesel Electric Plant to supply its electric energy requirements. During a 24 hr period, the plant consumed 250 gallons of fuel at 80 F and produced 2700 kw-hrs. Industrial fuel used is 30 API and was purchased at P3.00 per liter at 60 F. Determine the over-all efficiency of the plant.A. 25.06%B. 29.07%C. 26.08%D. 30.01%Solution:

Solving for :

Solving for :

Then,

=0.2608=26.08%26. A certain coal has the following ultimate analysis:A = 5%C = 70%H2 = 2.5%M = 10%N2 = 4%S = 5%Q2 = 3.5%Find actual air-fuel for an excess air of 30%.A. 11.67B. 9.54C. 15.4D. 13.75Solution:

For an excess air = 30%

27. It is required to find the theoretical volume of air at 20 C and 100 kPa absolute pressure to burn one kilogram coal. The ultimate analysis of coal as-fired is as follows:C = 65.65%O = 18.61%S = 1.51%Moist. = 3%H = 5.87%N = 1.3%Ash = 5.36%A. 9.43 m3air/kgcoalB. 7.43 m3air/kgcoalC. 8.43 m3air/kgcoalD. 6.43 m3air/kgcoalSolution:The theoretical volume of air required;

Solving for :

28. A steam boiler burns fuel oil with 30% excess air and represented as C16H32. The fuel gas leaves the preheater at 220 kPa. Find the actual-air fuel ratio.A. 15.6B. 19.2C. 16.75D. 18.01Solution:

By Formula

29. In burning a typical coal, the theoretical air-fuel ratio was found to be 15 kg/kg. The approximate heating value of the coal in kJ/kg is,A. 40,650B. 45,610C. 46,500D. 41,510Solution:

INTERNAL COMBUSTION ENGINE30. Determine the thermal efficiency of an air standard Otto cycle with 10% clearance.A. 53.89%B. 61.68%C. 58.33%D. 72.33%Solution:

31. A two-stroke Diesel engine has a friction power of 13% of the heat generated. Determine the brake thermal efficiency if the indicated thermal efficiency of the engine is 50%.A. 33%B. 37%C. 34%D. 36%Solution:

or 37%32. During a Morse test on a four-cylinder automotive engine, the speed was kept constant at 24.5 rps by the brake and the following brake torque readings were obtained:All cylinders firing193.8 N-mNo. 1 cylinder cut-out130.8 N-mNo. 2 cylinder cut-out130.2 N-mNo. 3 cylinder cut-out129.9 N-mNo. 4 cylinder cut-out131.1 N-mAccount for the frictional power, in kW.A. 8.72B. 9.13C. 10.15D. 12.07Solution:

No. 1 cylinder cut-out:

No. 2 cylinder cut-out:

No. 3 cylinder cut-out:

No. 4 cylinder cut-out:

33. An engine burns a liter of fuel each 12 min. The fuel has a specific gravity of 0.8 and a heating value of 45 MJ/kg. The thermal efficiency of the engine is 25%. What is the brake horsepower of the engine?A. 11B. 17C. 13D. 15Solution:

34. A Diesel engine used 27 tons of fuel per day when developing 4960 kW indicated power and 4060 kW brake power. Of the total heat supplied to the engine, 31.7% is carried away by cooling water and radiation, and 30.8% in the exhaust gases. Calculate the indicated thermal efficiency.A. 37.5%B. 35.7%C. 31.25%D. 32.75%Solution:

35. The combined mechanical electrical efficiency of an engine-generator set is 82%. If the combined specific fuel consumption is 0.205 kg/kW-hr, the indicated specific fuel consumption is,A. 0.235 kg/kW-hrB. 0.25 kg/kW-hrC. 0.168 kg/kW-hrD. 0.175 kg/kW-hrSolution:

= 0.168 kg/kW-hr36. The thermal efficiency of an engine is 30% and the fuel used have a heating value of 40,500 kJ/kg. The engines specific fuel consumption is,A. 3.375 kg/kW-hrB. 0.285 kg/kW-hrC. 0.296 kg/kW-hrD. 0.375 kg/kW-hrSolution:

37. A car engine produces an average of 25 kW of power in a period of 10 min. during which 1.25 kg of gasoline is consumed. If the heating value of gasoline is 43,000 kJ/kg, the efficiency of this engine during the period is,A. 24%B. 28%C. 32%D. 36%Solution:

38. An engine burns a liter of fuel each 12 minutes. The fuel has a relative density 0.8 and a heating value of 45 MJ/kg. The engine has a brake thermal efficiency of 25%. What is the brake horsepower of the engine?A. 16.76B. 12.68C. 13.56D. 28.34Solution:1 Liter = 0.001 m3

39. A 500 kW Diesel engine develops torque of 2 kN-m. The engine drives an alternating current generator with 8 poles producing current at 60 Hz. What is the speed ratio of reduction gear?A. 3.6:1B. 1.6:1C. 2.6:1D. 4.6:1Solution:

Thus, the speed ratio is

40. A 1500 kW diesel engine operates at an altitude of 1200 meters elevation. Find the power developed by the engine at higher elevation.A. 1100 kwB. 1285 kwC. 1195 kwD. 1205 kwSolution:Considering the effect of both pressure and temperature change:

Brake power at a higher elevation = Brake power at a lower elevation

= pressure at a higher elevation

= pressure at sea level (standard)

= temperature at a higher elevation

= temperature at a lower elevation (standard)

For every 1000 feet above sea level;Decrease in pressure is 1 inch Hg absoluteDecrease in temperature is 3.566 degrees Rankine

41. Determine the power output of a Diesel power plant if the engine and generator efficiency is 83% and 95% respectively. The engine uses 25o API fuel and has a fuel consumption of 228 kg/hr.A. 2815 kwB. 2500 kwC. 2650 kwD. 2750 kwSolution:

= engine mechanical efficiency = 83%

= generator efficiency = 95%

42. An engine developing 30 hp, is transferring 10 hp more to the cooling tower. If the top water and bottom water of the radiator are 200 F and 190 F, respectively, calculate the required water flow rate in gallons per minute.A. 20.34B. 15.25C. 5.08D. 10.17Solution:

In gpm:

43. The efficiency of an Otto engine is 55% and the stroke volume is 35 liters. If the heat added at the beginning of the combustion is 12.6 kJ, calculate the mean effective pressure.A. 194 kPaB. 188 kPaC. 198 kPaD. 184 kPaSolution:

Where;

Solving for :

Thus,

44. A test bed, 16-cylinder, V-type, turbo-charged Diesel engine developed 9,961 metric horsepower at 514 rpm. Heat rejection to lubricating oil is 76 kCal per metric hp-hr. Specific gravity of lubricating oil used is 0.90 and specific heat of oil is 0.50 Btu/lb-F. Compute the quantity of lubricating oil circulated in m3/hr if the temperature of lubricating oil entering the engine is 55 C and 65 C leaving.A. 258.34 m3/hrB. 123.45 m3/hrC. 168.23 m3/hrD. 324.56 m3/hrSolution:

Solving for mass flow rate of lubricating oil:

= heat carried away by lubricating oil = (9961)(76) = 757,036 kCal/hr

Then;

45. In an ideal Otto cycle, the initial pressure and temperature of air are 100 kPa and 18 degree C. Determine the maximum pressure in the cycle if the maximum temperature in the cycle is 600 degree C, and the compression ratio is 8.A. 1890 kPaB. 2240 kPaC. 2400 kPaD. 1500 kPaSolution:

p1 = 100 kPaT1 = 18 + 273 = 291 KT3 = 600 + 273 = 873 Krk = V1/V2 = 8

46. Air enters the cylinder of an internal combustion engine at an initial pressure and temperature of 95 kPa and 28 deg C. A four cylinder, single-acting, 40 mm x 55 mm, four stroke engine runs at 4500 rpm. The mass flow rate of air per seconds is 0.01 kg. What is the volumetric efficiency of the engine?A. 72%B. 81%C. 87%D. 97.7%Solution:

47. A 20 cm x 36 cm, twin cylinder, two stroke cycle diesel engine running at 650 rpm. The engine rate is 112 kw. Determine the engine displacement in cubic meter/sec per brake horsepower.A. 0.0163B. 0.16300C. 0.00163D. 0.0631Solution:

48. A 1000 kw-hr diesel generating set has a generator efficiency of 85%. If the mass of the fuel is 150 kg, compute the engine fuel rate.A. 0.15 kg/kw-hrB. 0.1175 kg/kw-hrC. 0.127 kg/kw-hrD. 22.7 kg/kw-hrSolution:

49. In an air standard diesel cycle, compression starts at 100 kPa and 303 K. The compression ratio is 20 to 1. The maximum cycle temperature is 2200 K. Determine the thermal efficiency.A. 46%B. 64%C. 69%D. 70%Solution:

50. If the pressure at the beginning and end of compression in an Otto cycle engine are 100 kPa and 950 kPa, respectively, the maximum cycle temperature is 1500 K. Determine the air standard efficiency.A. 35.7%B. 39.5%C. 47.5%D. 57.7%Solution:

(c)51. An Otto engine has a clearance volume of 8%. It produces 500 kw power. Compression starts at 100 kPa and 25 C. What is the heat rejected in kw?A. 273 kwB. 372 kwC. 327 kwD. 732 kwSolution:

52. The following data are the results on a test of a two cylinder, four stroke cycle Otto engine: torque = 2000 N-m; indicated mean effective pressure = 700 kPa; fuel consumption = 0.006 kg/sec; fuel heating value = 43,000 kJ/kg; bore x stroke = 30 cm x 40 xm; speed = 600 rpm. Calculate the brake mean effective pressure.A. 375 kPaB. 325 kPaC. 445 kPaD. 285 kPaSolution:

53. A four-cylinder, four-cycle engine with 10-cm diameter pistons and a 16-cm stroke operates at a speed of 600 rpm and yields an indicator diagram. The area under the curve (pV diagram) is equal to 12.0 cm2. The length of the diagram is 9.0 cm, and the spring constant of the indicator spring is 600 kPa/cm. Determine the mean effective pressure.A. 800 kPaB. 400 kPaC. 600 kPaD. 950 kPaSolution:

54. The compression ratio of an air-standard gasoline engine is 7.5. The heat added is 1890 kJ/kg. If the initial pressure and temperature are 1 bar and 27 C respectively, determine the temperature in C at the end of the isentropic expansion.A. 1206B. 2968C. 1765D. 1347Solution:

T1 = 27 + 273 = 300 Krk = 7.5QA/m = 1890 kJ/kg

55. Calculate the thermal efficiency of an air-standard Diesel cycle operating with a compression ratio of 21 and cut-off ratio of 3.A. 55.9%B. 61.4%C. 66.9%D. 71.9%Solution:

GAS TURBINE POWER PLANT56. A gas turbine plant working on a closed air-standard Brayton cycle has a pressure ratio of 5. The heat rejected in the heat sink is 2000 kW. If one-fifth of the expansion work is supplied for compression ideally, determine the theoretical power of the gas turbine.A. 1460 kWB. 740 kWC. 1260 kWD. 1640 kWSolution:

57. A gas turbine power plant operating in a Brayton cycle, the compressor power needed is 250 kW which is driven by a 1000 kW turbine. The compressor efficiency is 90% and that of the turbine is 90%. Determine the back work ratio.A. 30%B. 34%C. 25%D. 40%Solution:Back work ratio = compressor power / turbine power = 250 kw / 1000 kw = 0.25 = 25% 58. A gas turbine plant utilizing a closed cycle has the following temperatures at each state point: T1 = 90 F, T2 = 590 F, T3 = 1440 F, and T4 = 530 F. Based on these values, calculate the thermal efficiency of the cycle.A. 48%B. 45%C. 46%D. 47%Solution:

or 48%59. In a simple gas turbine plant working on the ideal constant pressure cycle, air is taken into the compressor at 1 bar, 16 C and delivered at 5.4 bar. If the temperature at turbine inlet is 700 C, calculate the ideal thermal efficiency. Take k = 1.4.A. 35.28%B. 42.61%C. 38.23%D. 45.66%Solution:

Solving for , , and :

Then;

60. The net power output of an air-standard Brayton cycle is 200 kW. Air enters the compressors at 32 C and leaves the high-temperature heat exchanger at 800 C. What is the mass flow rate of air if it leaves the turbines at 350 C.A. 0.57 kg/sB. 0.67 kg/sC. 0.87 kg/sD. 0.77 kg/sSolution:

Solving for and .

Then;

61. Air enters the compressor of a gas turbine at 110 kPa and 27 C with a volume flow rate of 8.5 m3/sec. The compressor pressure ratio is 10 and its isentropic efficiency is 82%. At the inlet to the turbine, the pressure is 950 kPa and the temperature is 1400 K. The turbine has an isentropic efficiency of 85% and the exit pressure is 100 kPa. On the basis of an air standard analysis, what is the thermal efficiency of the cycle in percent?A. 27.3B. 22.0C. 21.8D. 20.2Solution: p1 = 110 kPa, T1 = 27 + 273 = 300 KV1 = 8.5 m3/secp2/p1 = 10, c = 0.82p3 = 950 kPa, p4 = 100 kPa, t = 0.85T3 = 1400 K

62. Air enters a gas turbine power plant at 1 bar and 30 C with a volume flow rate of 5 m3/s. The compressor pressure is 10 and its isentropic efficiency is 80%. The turbine inlet pressure and temperature are 1000 kPa and 1300 C, respectively. The turbine isentropic efficiency is 85% and the exit pressure is 100 kPa. Determine the thermal efficiency of the cycle in percent?A. 52.9%B. 39.5%C. 29.5%D. 92.5%Solution: p1 = 1 bar = 100 kPaT1 = 30 + 273 = 303 KV1 = 5 m3/sp2/p1 = 10c = 0.80p3 = 1000 kPaT3 = 1300 + 273 = 1573 Kht = 0.85p4 = 100 kPa

63. A 75 MW stationary gas turbine power plant has air enters the compressor at 100 kPa, 300 K temperature and pressure ratio of 10. The turbine inlet temperature is 1650 K. Using the standard Brayton cycle, determine the back-work ratio of the gas turbine power plant.A. 0.255B. 0.879C. 1.061D. 0.351Solution: p1 = 100 kPaT1 = 300 KT3 = 1650 Kp2/p1 = p3/p4 = 10

64. A 20,000 MW gas turbine operating in the simple open cycle has an exhaust gas flow of 100 kg per second. The gas enters a waste heat recovery boiler at 450 C and leaves at 180 C, specific heat of the gas is 0.85 kJ/kg-K, heat required to produced 1 kg of steam at 4.5 MPa and 320 C from feedwater at 110 C is 5.5 kJ. Calculate the quantity of steam that can be produce in kg per second.A. 4173 kg/sB. 1723 kg/sC. 2173 kg/sD. 3173 kg/sSolution: Heat rejected = heat absorbed

65. A simple Brayton cycle which uses helium as the working fluid, has a maximum temperature of 1150 K, and a pressure ratio of 2.90. At the start of the compression, the helium pressure and temperature are 90 kPa and 300 K. Based upon cold air-standard analysis assumptions, determine the thermal efficiency of the cycle in percent?A. 34.7%B. 17.5%C. 23.7%D. 28.7%Solution: k = 1.667 for heliump1 = 90 kPaT1 = 300 KT3 = 1150 Kp2/p1 = p3/p4 = 2.9

66. The mass flow rate of the gas in a gas turbine is 30 kg/sec. The specific enthalpy and velocity in the inlet are 1300 kJ/kg and 200 m/sec respectively while in the outlet are 300 kJ/kg and 50 m/s, respectively. Calculate the power output in kw of the turbine if there is a heat loss of 3 MW.A. 32,678.50 kwB. 27,562.50 kwC. 37,125.50 kwD. 45,500.50 kwSolution:

67. An ideal gas turbine operates with a pressure ratio of 7.5 and temperature limits of 25 C and 1100 C. The energy input in the high temperature heat exchanger is 500 kw. Determine the air flow rate in kg/hr.A. 59.3B. 2135C. 235D. 3450Solution: p2/p1 = 7.5T1 = 25 + 273 = 298 KT3 = 1100 + 273 = 1373 K

68. Air at 400 kPa and 590 K is extracted from a jet engine compressor to be used for the generation of auxiliary power for the cabin. The extracted air is cooled in a constant pressure heat exchanger down to 460 K. It then enters an isentropic turbine and expands to 100 kPa before being rejected into the cabin. If the mass flow is 15 kg/min, determine the power developed by the turbine in kw.A. 63.7 kwB. 73.6 kwC. 37.6 kwD. 76.3 kwSolution: T2 = 590 K, T3 = 460 Kp4 = 100 kPa, p3 = 400 kPam = 15 kg/min

Power developed by the turbine = mcp(T3 T4)= (15/60)(1.0)(460 309.56) = 37.61 kW69. The mass flow rate of the gas in gas turbine is 40 kg/sec. The specific enthalpy and velocity in the inlet are 1600 kJ/kg and 200 m/sec respectively while the outlet are 500 kJ/kg and 50 m/sec, respectively. Calculate the power output in kw of the turbine if there is a heat loss of 1.5 MW.A. 37,462B. 40,872C. 43,250D. 34,605Solution:

70. An ideal gas turbine operates with a pressure ratio of 9 and temperature limits of 25 C and 1100 C. The energy input in the high temperature heat exchanger is 300 kw. Determine the air flow rate in kg/hr.A. 1650B. 1859C. 1325D. 1732Solution: p2/p1 = 9T1 = 25 + 273 = 298 KT3 = 1100 + 273 = 1373 K

STEAM POWER PLANT

71. The energy input to the turbine is 2800 kJ/kg and the energy at the exit is 1400 kJ/kg, efficiency of the engine is 75% and power output at full load is 6000 kW. What is the turbine flow rate at full load in kg/kW-hr?A. 5.97B. 4.33C. 3.43D. 9.23Solution:

72. A water-tube condenser has a total of 90 tubes. If these type of condenser are two passes, then compute the number of tubes per pass.A. 45 tubesB. 30 tubesC. 60 tubesD. 180 tubesSolution: For two pass. The number of tubes per pass = 90 tubes / 2 pass = 45 tubes 73. A steam condenser receives 10 kgs per second of steam with an enthalpy of 2570 kJ/kg. Steam condensers into a liquid and leaves with an enthalpy of 160 kJ/kg. Cooling water passes through the condenser with temperature increases from 13 degree C to 24 degree C. Calculate the cooling water flow rate in kgs per second.A. 533.2B. 518.4C. 528.9D. 523.2Solution:

74. In a steam Rankine cycle, saturated liquid at 14.7 psia (vf = 0.01672 cu. ft. per lb,) is pump to a high pressure liquid at 100 psia. How much work is required to pump one lbm of water?A. 118 BtuB. 18.5 BtuC. 0.129 BtuD. 0.264 BtuSolution:

75. A steam power plant has a turbine work of 320 kJ/kg and the pump work is 2 kJ/kg. If the mass flow rate is 10 kg per second, compute the power produced by this plant?A. 3200 kwB. 3220 kwC. 3180 kwD. 2080 kwSolution:

76. A turbine has an efficiency of 75% and has a steam flow rate of 22,000 kg/hr. If the available energy is 1200 kJ/kg, determine the kilowatt output at full load.A. 5500B. 3500C. 4500D. 4000Solution:

77. The available energy of a turbine is 1450 kJ/kg, efficiency of the engine is 70% and the power output at full load is 5.5 MW. What is the engine flow rate at full load in kg/kW-hr?A. 2.5B. 3.5C. 3.0D. 2.75Solution:

78. A steam plant operates with an initial pressure of 1.7 MPa and 370 C temperature and to a condenser at 170 kPa. If the turbine efficiency and boiler efficiency are 75% and 85%, respectively, determine the cycle thermal efficiency.Steam properties:At 1.70 MPa & 370 C:h = 3187.1 kJ/kgs = 7.1081 kJ/kgAt 170 kPa:hf = 483.20hfg = 2216.0sf = 1.4752 sfg = 5.7062A. 25.6%B. 52.6%C. 12.1%D. 35.6%Solution:

Assume water density at 1000 kg/m3.

79. Naga private power plant is using water as the working fluid that operates on an ideal Rankine cycle. Superheated vapor enters the turbine at 10,000 kPa and 520 C and is exhausted into the condenser at 8 kPa. The net output of the Rankine cycle is 100,000 kW. Determine the mass flow rate of steam in kg per second.Steam properties:At 10,000 kPa (100 bar) and 520 C:h = 3425.1, s = 6.622At 8 kPa: hf = 173.88, sf = 0.5926hg = 2577, sg = 8.2287vf = 0.0010084A. 967 kg/secB. 267 kg/secC. 74.4 kg/secD. 20.1 kg/secSolution:

80. A 15,000 kW steam turbine-generator power plant has full load steam rate of 7.5 kg/kW-hr. No load steam consumption is around 10% of full load steam consumption. Calculate the hourly steam consumption at three-fourths load in kg/hr.A. 112,500 kg/hrB. 15,500 kg/hrC. 87,187.50 kg/hrD. 6,750 kg/hrSolution:

At full load

At no load

Then,

At load,

81. A typical steam generator with an efficiency of 85% is producing 18 kg/sec of steam. The enthalpy of the entering water is 140 kJ/kg and is superheated to an enthalpy of 3300.50 kJ/kg. The fuel used has a heating value of 44,500 kJ/kg. The A/F ratio by weight is 20. Determine the amount of air needed in kg/hr.A. 168,317B. 178,328C. 96,123D. 108,288Solution:

82. A 12,000 kW steam turbine-generator power plant has full load steam rate of 5.5 kg/kW-hr. No load steam consumption is around 10% of full load steam consumption. Calculate the hourly steam consumption at two-third of load in kg/hr.A. 40,250B. 36,830C. 46,200D. 35,820Solution:

At full load

At no load

Then,

At load,

83. A condenser gauge reads 25.5 in Hg vacuum when the barometer stands at 10.32 m of H2O. Determine the absolute pressure in the condenser in mm Hg.A. 78.9 mm HgB. 235.6 mm HgC. 157.6 mm HgD. 111.6 mm HgSolution:

84. Steam at a pressure of 1 MPa (hf = 768.81 kJ/kg, hfg = 2015.3 kJ/kg) in the main steam line is passed through a throttling calorimeter with an absolute pressure of 110 kPa and a temperature of 105 C (h = 2685.15 kJ/kg). Calculate the steam quality.A. 95.39%B. 93.95%C. 99.53%D. 91.35%Solution:

85. A steam turbine is powered by a set of fixed orifice nozzles. Each has an isentropic efficiency of 90%. 176.67 C sat. steam (hg = 2773.10 kJkg) at 85.4 m/s enters the nozzles. The steam expands adiabatically to 533.5 m/s. What is the enthalpy of the steam as it leaves the nozzles?A. 2619 kJ/kgB. 2643 kJ/kgC. 2634 kJ/kgD. 2691 kJ/kgSolution:

86. An industrial plant operates a 5000 kW turbine having an engine efficiency of 73%. The initial steam conditions are at 3002.4 kJ/kg enthalpy and 6.4200 kJ/kg-K entropy. The back pressure is 3.4 kPa (sf = 0.38 kJ/kg-K, sg = 8.5246 kJ/kg-K, hf = 109.32 kJ/kg, hg = 2546.82 kJ/kg. The turbine steam rate in kg/kw-hr is,A. 3.32B. 4.54C. 3.23D. 4.45Solution:

87. A water tube boiler has a heating surface area of 500 m2. For a developed boiler hp of 825. Determine the percent rating of the boiler.A. 162.45%B. 148.98%C. 153.37%D. 142.18%Solution:500 m2 = 5383 ft2Dev. Bo. Hp. = 825 Rated Bo. Hp. = 5383 / 10 = 538.3 Percent rating = Dev. Bo. Hp. / Rated Bo. Hp. = (825 / 538.3 )(100%) = 153.26%88. 19 liters per min of hot water at 82 C (vf = 1.0305 x 10-3 m3/kg) is produced in a flow system by injection and condensation of low pressure steam at 138.675 kPag and 80% quality into cold water at 16 C. Calculate the steam flow rate in kg/min. @ 138.675 kPag, hf = 529.65 kJ/kg, hg = 2715.0 kJ/kg.A. 3.69B. 14.75C. 2.80D. 10.45Solution:

At 80 % quality

89. After expanding 2.5 L of superheated steam at 2.5 MPaa and 400 C, its pressure was decreased to 0.01 MPaa. If its dryness fraction is 90%, what is the final volume of the steam in L? @ 2.5 MPaa & 400 C, v = 125.2 x 10-3 m3/kg. @ 0.01 MPaa, vf = 1.0102 x 10-3 m3/kg, vg = 14,674 x 10-3 m3/kg.A. 264B. 164C. 364D. 464Solution:

90. The equivalent evaporation of a boiler, from and at 100 C is 15 kg steam per kg fuel and the calorific value of the fuel burned is 41.9 MJ/kg. What is the boiler efficiency? @ 2.5 MPaa & 400 C; hfg = 2257 kJ/kg.A. 88.0%B. 80.8%C. 84.8%D. 82.0%Solution:

91. In a steam power plant, the capacity is 20 MW and 5% is for auxiliaries. If the energy charged to the station is 100 MW and the boiler efficiency is 75%, the gross station heat rate in kJ/kW-hr is ___.A. 14,210B. 13,500C. 18,950D. 18,000Solution:

92. The power developed by the steam turbine is 2800 kW while the power required by the feedwater pump is 12 kW. If the heat supplied to the boiler is 3500 kJ/kg and the heat rejected from the condenser is 2200 kJ/kg, find the mass flow rate of the steam in kg/s.A. 2.1B. 1.7C. 2.5D. 3.1Solution:

93. Determine the work of a pump in kJ required in raising the pressure of 10 kg of water from 20 kPaa to 3 MPaa, assuming that the specific volume of saturated water at 20 kPaa is 1.017 x 10-3 m3/kg.A. 30.3B. 2.65C. 3.03D. 26.5Solution:

94. Given the steam pressure of 900 lb/ft2, temperature of 300 F, specific volume of 5.8 ft3/lb. If the specific enthalpy is 9500 ft-lb/lb. What is the internal energy per pound of the system?A. 4400 ft-lbB. 3900 ft-lbC. 4280 ft-lbD. 3400 ft-lbSolution:

95. Determine the heat transferred to the cooling fluid in a condenser operating under steady flow conditions with steam entering with an enthalpy of 2300 kJ/kg and a velocity of 350 m/s. The condensate leaves with an enthalpy of 160 kJ/kg and velocity of 70 m/s.A. -1992 kJ/kgB. 2190 kJ/kgC. -2199 kJ/kgD. 2910 kJ/kgSolution:

96. Steam at the rate of 500 kg/hr is produced by a boiler from 40 C feedwater. If the enthalpy of the steam is 2512 kJ/kg, find the hourly rate of heat required.A. 1,151,370B. 1,134,270C. 1,172,264D. 1,121,274Solution:

97. A simple Rankine cycle operates between superheated steam at 6 MPa. 600 C entering the turbine, and 10 kPa entering the pump. Determine the maximum possible cycle thermal efficiency. Steam properties: at 6 MPa, 600 C, h = 3658, s = 7.1685; at 10 kPa, hf = 192, hfg = 2393, sf = 0.649, sfg = 7.502, vf = 0.001 m3/kg.A. 35.0B. 37.5C. 40.0D. 42.5Solution:

98. An open feedwater heater utilizes saturated steam at 150 C extracted from the steam turbine. Feedwater to be heated enters at 60 C. If the mixture leaves the heater at the rate of 18000 kg/hr, calculate for the quantity of steam extracted from the turbine, in kg/hr. Steam properties at 150 C, hf = 632.2, hfg = 2114.3; at 60 C, hf = 251.13.A. 2974B. 2749C. 4279D. 4792Solution:

Energy balance

At 150 C

At 60 C

99. A steam generating unit produces steam at the rate of 10 kg/s at 5 MPa, 450 C which is continuously blown down at 0.25 kg/s. Feedwater enters the economizer at 100 C. Coal with a heating value of 42,000 kJ/kg as fired is burned at the rate of 1 kg/s. What is the over-all efficiency of the steam boiler? Steam properties at 5 MPa, 450 C, h = 3316.2; at 5 MPa, 100 C, h = 422.72; at 5 MPa, hf = 1154.23, hg = 2794.3.A. 69.33B. 63.39C. 66.36D. 72.30Solution:

Over-all boiler efficiency, eo.

(c).100. A horizontal return tubular boiler with a heating surface of 2000 m2 generates steam at the rate of 4.5 kg/s. Feedwater enters at 5 MPa, 120 C and steam leaves at 5 MPa, 350 C. Calculate for the percent rating developed if coal with a heating value of 20,000 kJ/kg is burned at the rate of 9 Mtons/hr. Steam properties at 5 MPa, 350 C, h = 3068.4; at 5 MPa, 120 C, h = 507.09.A. 62.46B. 66.78C. 64.62D. 68.94Solution:For fire tube boiler

Developed boiler hp:

Percent rating

101. A 5-MW steam turbine generator power plant has a full-load steam rate of 6.0 kg/kW-hr. Assuming that no-load steam consumption as 10% of full-load steam consumption, compute for the hourly steam consumption at 60% load, in kg/he.A. 12,900B. 25,500C. 19,200D. 31,800Solution:At full loadSteam consumption, ms2ms2 = (5000 kw)(6.0 kg/kW-hr) = 30,000 kg/hrAt no-loadSteam consumption, ms1ms1 = (0.10)(30,000 kg/hr) = 3,000 kg/hrUsing two-point form:

Where:P1(x1,y1) = P1(0,3000)P2(x2,y2) = P2(5000,30000)P(x,y) = P(ms,L)Thusms = 5.4L + 3000At 60 % load, L = 0.6(5000) = 3000ms = 5.4(3000) + 3000 = 19,200 kg/hr 102. The vacuum in the surface condenser of a small condensing steam power plant is 640 mm Hg as referred to a 760 mm Hg barometer. If the temperature in the condenser is 35 C (corresponding pressure of 5.628 kPa), the vacuum efficiency is approximately:A. 81.96B. 86.19C. 89.16D. 93.39Solution:

patm = 760 mm Hgpcond = 640 mm Hg vac = 120 mm Hgpsat = 5.628 kPa (760 mm Hg / 101.325 kPa) = 42.21 mm Hg

103. A boiler feedpump receives water at 200 C (enthalpy, h = 850 kJ/kg) from a surface condenser at the rate of 100 L/s. It operates against a total head of 850 meters. Determine the enthalpy leaving the pump, in kJ/kg.A. 878.5B. 899.2C. 857.8D. 919.9Solution:Pump work, WpWp = m(h2 h1) = mgh/1000h2 850 = (9.81)(800)/1000h2 = 857.8 kJ/kg 104. A binary mercury-steam cycle produces a net power output of 30 MW. Steam enters the turbine at 4 MPa, 400 C where it is being exhausted to a condenser pressure of 10 kPa. Assuming an overall thermal efficiency of 80% for the cycle and 100% heat transfer efficiency in the heat exchanger, determine the enthalpy difference in the boiler per kilogram of mercury per second. Steam properties at 4 MPa, 400 C, h = 3213.6, s = 6.769; at 10 kPa, hf = 191.83, hfg = 2392.8, sf = 0.6394, sfg = 7.5009.A. 37,500B. 30,000C. 32,500D. 35,000Solution:

105. In a co-generation steam power plant, steam enters the turbine at 5 MPa, 400 C. A quarter of the steam is extracted from the turbine at 170 kPa while the remaining steam is allowed to expand to 10 kPa. The extracted steam is then condensed and mixed with feedwater at constant pressure. The mixture is then pumped to a boiler pressure of 5 MPa. Mass flowrate of steam through the boiler is 25 kg/s. Assuming no pressure drops and heat losses in the piping system, calculate for the process heat required in kW. Steam properties at 5 MPa, 400 C, h = 3195.7, s = 6.6459; at 0.17 MPa, hf = 483.2, hfg = 2216, sf = 1.4752, sfg = 5.7062; at 0.01 MPa, hf = 191.83, hfg = 2392.8, sf = 0.6493, sfg = 7.5009.A. 12,551B. 11,255C. 13,829D. 15,125Solution:s1 = s2 = 6.6459 = 1.4752 + x2(5.7062)x2 = 0.9062h2 = hf2 + x2hfg2 = 483.2 + 0.9062(2216) = 2491.34Qph = m(h2 h3) = (25/4)(2491.34 483.2) = 12,550.875 kW

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