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Section-1: Basic and Modified Rankine Cycles

9-1-1 [carnot-9kPa] Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a pressure of 10 MPa, and enters the turbine as saturated vapor. The condenser pressure is 9 kPa. Determine (a) the thermal efficiency, (b) the back work ratio, (c) the heat transfer to the working fluid per unit mass passing through the boiler in kJ/kg and (d) the heat transfer from the working fluid per unit mass passing through the condenser in kJ/kg. (e) What-if Scenario: What would the thermal efficiency be if the steam entered the turbine at 5 MPa and the condenser pressure were 90 kPa ? [Edit Problem] [TEST Solution] Answers: (a) 45.7%, (b) 0.37, (c) 1317 kJ/kg, (d) 714.5 kJ/kg, (e) 31.1%

Anim. 9-1-1(click)

9-1-2 [carnot-800kPa] Water enters the boiler of a steady flow Carnot engine as a saturated liquid at 800 kPa, and leaves with a quality of 0.95. Steam leaves the turbine at a pressure of 100 kPa. Determine (a) the thermal efficiency and (b) the net work output. Answers: (a) 15.9%, (b) 310.5 kW

[Edit Problem] [TEST Solution]

9-1-3 [carnot-10MPa] Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a pressure of 10 MPa, and saturated vapor enters the turbine. The condenser pressure is 8 kPa. The effects of irreversibilities in the adiabatic expansion and the compression processes are taken into consideration. The turbine and pump efficiencies are 80% and 75%, respectively. Determine (a) the thermal efficiency, (b) the back work ratio, (c) the heat transfer to the working fluid per unit mass passing through the boiler in kJ/kg and (d) the heat transfer from the working fluid per unit mass passing through the condenser in kJ/kg. [Edit Problem] [TEST Solution] Answers: (a) 24.4%, (b) 0.62, (c) 1196 kJ/kg, (d) 903 kJ/kg

9-1-4 [steam-4MPa] Consider a steam power plant operating on the simple ideal Rankine cycle. The steam enters the turbine at 4 MPa, 400 o C and is condensed in the condenser at a pressure of 100 kPa. Determine (a) the thermal efficiency of the cycle. (b) What-if Scenario: What would the thermal efficiency be if steam entered the turbine at 5 MPa and the condenser pressure were 90 kPa? [Edit Problem] [TEST Solution] Answers: (a) 27%, (b) 28.6%

Anim. 9-1-4(click)

9-1-5 [steam-500C] A steam power plant operates on the simple ideal Rankine cycle. Steam enters the turbine at 4 MPa, 500 o C and is condensed in the condenser at a temperature of 40 o C. (a) Show the cycle on a T-s diagram. If the mass flow rate is 10 kg/s, determine (b) the thermal efficiency of the cycle and (c) the net power output in MW. [Edit Problem] [TEST Solution] Answers: (b) 37.64%, (c) 12.324 MW

9-1-6 [steam-69MPa] Water is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 6.9 MPa. The condenser pressure is 6.9 kPa. Determine (a) the net work per unit mass of steam flow in kJ/kg, (b) the heat transfer to the steam passing through the boiler in kJ/kg, (c) the thermal efficiency and (d) the back work ratio. [Edit Problem] [TEST Solution] Answers: (a) 962 kJ/kg, (b) 2604 kJ/kg, (c) 36.9%, (d) 0.00715

9-1-7 [steam-5MPa] Consider a steam power plant operating on the ideal Rankine cycle. The steam enters the turbine at 5 MPa, 350 o C and is condensed in the condenser at a pressure of 15 kPa. Determine (a) the thermal efficiency of the cycle. (b) What-if Scenario: What would the thermal efficiency be if steam were superheated to 750 o C instead of 350 o C ? [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 34.3%, (b) 40.6%

9-1-8 [steam-9MPa] Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 9 MPa and saturated liquid exits the condenser at 0.009 MPa. The net power output of the cycle is 100 MW. Determine (a) the thermal efficiency of the cycle, (b) the back work ratio, (c) the mass flow rate of steam, (d) the heat transfer into the working fluid as it passes through the boiler and (e) the heat transfer from the condenser to the steam as it passes through the condenser. [Edit Problem] [TEST Solution] Answers: (a) 37%, (b) 95%, (c) 105.6 kg/s, (d) 269.2 MW, (e) 169.1 MW

9-1-9 [steam-10MPa] Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 10 MPa and saturated liquid exits the condenser at 0.01 MPa. The net power output of the cycle is 150 MW. The turbine and the pump each have an isentropic efficiency of 85%. Determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of steam, (c) the heat transfer into the working fluid as it passes through the boiler and (d) the heat transfer from the condenser to the steam as it passes through the condenser. [Edit Problem] [TEST Solution] Answers: (a) 31.5%, (b) 189 kg/s, (c) 476.4 MW, (d) 326.2 MW

Anim. 9-1-9(click)

9-1-10 [propane-10MPa] Propane is the working fluid in a supercritical power plant. The turbine inlet pressure is 10 MPa, the temperature is 150 o C and it exits at -30 o C. The net power output of the cycle is 2 kW. The turbine and the pump have isentropic efficiencies of 90% and 80%, respectively. Determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of propane. [Edit Problem] [TEST Solution] Answers: (a) 23.9%, (b) 0.016 kg/s

9-1-11 [water-12MPa] Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at 12 MPa and 500 o C. The condenser pressure is 8 kPa. The turbine and the pump have isentropic efficiencies of 85% and 75%, respectively. Determine (a) the thermal efficiency of the cycle, (b) the net power output, (c) the heat transfer into the working fluid as it passes through the boiler and (d) the heat transfer from the condenser to the steam as it passes through the condenser. (e) What-if Scenario: What would the net power output be if the mass flow rate of the working fluid were 100 kg/s ? [Edit Problem] [TEST Solution] Answers: (a) 35%, (b) 1.1 MW, (c) 3.1 MW, (d) 2.5 MW, (e) 110 MW

9-1-12 [steam-3MPa] In a steam power plant operating on a Rankine cycle, steam enters the turbine at 3 MPa, 350 o C and is condensed in the condenser at a pressure of 75 kPa. If the adiabatic efficiencies of the pump and turbine are 80% each, determine (a) the thermal efficiency of the cycle. (b) What-if Scenario: What would the thermal efficiency be if the boiler pressure were increased to 5 MPa? [Edit Problem] [TEST Solution] Answers: (a) 20.85%, (b) 22.8% Image of a steam power plant

9-1-13 [water-540C] Water is the working fluid in a vapor power plant. Superheated steam leaves the steam generator at 8.2 MPa, 540 o C and enters the turbine at 7.5 MPa, 500 o C. The steam expands through the turbine, exiting at 8 kPa with a quality of 94%. Condensate leaves the condenser at 5 kPa, 30 o C and is pumped to 9 MPa before entering the steam generator. The pump efficiency is 80%. Determine (a) the thermal efficiency of the cycle and (b) the net power developed. (c) What-if Scenario: What would the net power developed be if the mass flow rate of steam were 15 kg/s ? [Edit Problem] [TEST Solution] Answers: (a) 28.6%, (b) 960.15 kW, (c) 14.4 MW

9-1-14 [water-18MPa] Water is the working fluid in a vapor power plant. Superheated steam enters the turbine at 18 MPa and 580 o C. Steam expands through the turbine, exiting at 6 kPa and the turbine efficiency is 82%. Condensate leaves the condenser at 4.5 kPa, 25 o C and is pumped to 18.5 MPa before entering the steam generator. The pump efficiency is 77%. Determine (a) the net work per unit mass of steam flow, (b) the heat transfer per unit mass of steam passing through the boiler, (c) the thermal efficiency and (d) the heat transfer

per unit mass of steam passing through the condenser. (e) What-if Scenario: What would the thermal efficiency be if efficiencies of both the turbine and pump were 99% each? [Edit Problem] [TEST Solution] Answers: (a) 1204 kJ/kg, (b) 3370.7 kJ/kg, (c) 35.7%, (d) 2166.7 kJ/kg, (e) 43.3%

9-1-15 [steam-25MW] A steam power plant operates on the following cycle producing a net power of 25 MW. Steam enters the turbine at 16 MPa, 550 o C and enters the condenser as saturated mixture at 10 kPa. Subcooled liquid enters the pump at 9 kPa, 35 o C and leaves at 17 MPa, which then enters the boiler at 16.8 MPa, 33 o C and exits at 16.2 MPa, 575 o C. If the isentropic efficiency of the turbine is 90% and that of the pump is 83%, determine (a) the mass flow rate of steam and (b) the mass flow rate of cooling water in the [Edit Problem] [TEST Solution] condenser in which temperature rises from 20 o C to 30 o C. Answers: (a) 20.37 kg/s, (b) 995.1 kg/s

Anim. 9-1-15(click)

9-1-16 [water-4MPa] Water is the working fluid in a vapor power plant. Steam enters the turbine at 4 MPa, 540 o C and exits the turbine as a two-phase liquid vapor mixture at 27 o C. The condensate exits the condenser at 25 o C. The turbine efficiency is 90% and the pump efficiency is 80%. If the power developed is 1 MW, determine (a) the steam quality at the turbine exit, (b) the mass flow rate and (c) the thermal efficiency. [Edit Problem] [TEST Solution] Answers: (a) 0.89, (b) 0.8 kg/s, (c) 36%

9-1-17 [water-9MPa] Water is the working fluid in an ideal Rankine cycle. The pressure and temperature at the exit of the steam generator is 9 MPa and 480 o C. A throttle valve placed between the steam generator and the turbine reduces the turbine inlet pressure to 7 MPa. The condenser pressure is 7 kPa, and the mass flow rate of the steam is 170 kg/s. The turbine and the pump have an isentropic efficiency of 90% each. Determine (a) the net power developed, (b) the heat transfer to the steam passing through the boiler and (c) the thermal efficiency. (d) What-if Scenario: What would the net power developed be if the mass flow rate of steam were 100 kg/s ? [Edit Problem] [TEST Solution] Answers: (a) 190 MW, (b) 537 MW, (c) 35.4%, (d) 112 MW

9-1-18 [steam-16MPa] Consider a steam power plant operating on a reheat Rankine cycle. Steam enters the high pressure turbine at 16 MPa, 550 o C and is condensed in the condenser at 10 kPa. If the moisture content of the steam at the exit of the low pressure turbine is not to exceed 5%, determine (a) the pressure at which the steam should be reheated and (b) the thermal efficiency of the cycle. Assume the steam is reheated to the inlet temperature of the high pressure turbine. (c) What-if Scenario: What would the thermal efficiency be if the moisture tolerance of the turbine were increased to 10%? [Edit Problem] [TEST Solution] Answers: (a) 1.29 MPa, (b) 43.9%, (c) 44.3%

Anim. 9-1-18(click)

9-1-19 [reheat-9MPa] Consider a steam power plant that operates on a reheat Rankine cycle. Steam enters the high pressure turbine at 9 MPa, 600 o C and leaves as a saturated vapor. The steam is then reheated to 500 o C before entering the low pressure turbine, and is condensed in a condenser at 7 kPa. The mass flow rate is 150 kg/s. Determine (a) the net power developed, (b) the rate of heat transfer to the working fluid in the reheat process and (c) the thermal efficiency. (d) What-if Scenario: What would the rate of heat transfer [Edit Problem] [TEST Solution] be if steam were reheated to 550 o C ? Answers: (a) 270 MW, (b) 113.3 MW, (c) 42.6%, (d) 129 MW

9-1-20 [reheat-17MPa] Consider a steam power plant operating on an ideal Rankine cycle that has reheat at a pressure of one-fifth the pressure entering the high pressure turbine. Steam enters the high pressure turbine at 17 MPa and 500 o C. The steam is reheated to 500 o C before entering the low pressure turbine, and is condensed in a condenser at 10 kPa. Determine (a) the thermal efficiency and (b) the steam quality at the exit of the second turbine stage. [Edit Problem] [TEST Solution] Answers: (a) 43%, (d) 0.869

9-1-21 [reheat-2MPa] An ideal reheat cycle operates with steam as the working fluid. The reheat pressure is 2 MPa. Steam enters the high pressure turbine at 13 MPa and 600 o C. The steam is reheated to 600 o C before entering the low pressure turbine, and is condensed in a condenser at 6 kPa. Determine (a) the thermal efficiency and (b) the steam quality at the exit of the second turbine stage. (c) What-if Scenario: How would the answer in (b) change if the reheat pressure were 7 MPa? [Edit Problem] [TEST Solution] Answers: (a) 45.8%, (d) 0.91, (c) 0.84

9-1-22 [reheat-15MPa] In a steam power plant operating on a reheat Rankine cycle, steam enters the HP turbine at 15 MPa, 620 o C and is condensed in the condenser at a pressure of 15 kPa. If the moisture content in the turbine is not to exceed 10%, determine (a) the reheat pressure and (b) the thermal efficiency of the cycle. (c) What-if Scenario: What would the thermal efficiency be if the moisture tolerance of the turbine were increased to 15%? [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) (b) 44.46%, (c) 43.47% Image of a steam power plant

9-1-23 [reheat-10MPa] Steam is the working fluid in an ideal Rankine cycle with superheat and reheat. Steam enters the first stage turbine at 10 MPa, 500 o C and expands to 700 kPa. It is then reheated to 450 o C before entering the second stage turbine, where it expands to

the condenser pressure of 8 kPa. The net power output is 100 MW. Determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of steam and (c) the rate of heat transfer from the condensing steam as it passes through the condenser. [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 41.5%, (b) 62.5 kg/s, (c) 141.4 MW

9-1-24 [regen-9MPa] In a steam power plant operating on the ideal regenerative Rankine cycle with one open feedwater heater, steam enters the turbine at 9 MPa, 480 o C and is condensed in the condenser at a pressure of 7 kPa. Bleeding from the turbine to the FWH occurs at 0.7 MPa. The net power output of the cycle is 100 MW. Determine (a) the thermal efficiency of the cycle, (b) the mass flow rate entering the turbine and (c) the rate of heat transfer to the working fluid passing through the steam generator. (d) What-if Scenario: What would the net power developed be if the bleeding pressure were increased to 1.2 MPa? [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 43.3%, (b) 87.7 kg/s, (c) 230 MW, (d) 96 MW

Anim. 9-1-24(click)

9-1-25 [regen-15MPa] In a steam power plant operating on the ideal regenerative Rankine cycle with one open feedwater heater, steam enters the turbine at 15 MPa, 620 o C and is condensed in the condenser at a pressure of 15 kPa. Bleeding from the turbine to the FWH occurs at 1 MPa. Determine (a) the fraction of steam extracted and (b) the thermal efficiency of the cycle. (c) What-if Scenario: What would the thermal efficiency be if the bleeding pressure were increased to 1.5 MPa? [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 0.2045, (b) 45.5%, (c) 45.54%

9-1-26 [regen-11MPa] A power plant operates on a regenerative vapor power cycle with one open feedwater heater. Steam enters the first turbine stage at 11 MPa, 600 o C and expands to 1 MPa, where some of the steam is extracted and diverted to the open feedwater heater operating at 1 MPa. The remaining steam expands through the second turbine stage to a condenser pressure of 6 kPa. Saturated liquid exits the open feedwater heater at 1 MPa. The net power output is 264 MW. Determine (a) the thermal efficiency of the cycle, (b) the mass flow rate into the first turbine stage and (c) the fraction of flow extracted where bleeding occurs. (d) What-if Scenario: What would the net power developed be if the bleeding pressure were increased to 1.2 MPa? [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 46.3%, (b) 200 kg/s, (c) 0.2215, (d) 96 MW

9-1-27 [regen-14MPa] Consider a steam power plant operating on the ideal regenerative Rankine cycle with one open feedwater heater. Steam enters the turbine at 14 MPa, 610 o C and is condensed in the condenser at a pressure of 12 kPa. Some steam leaves the turbine at a pressure of 1.2 MPa and enters the open feedwater heater. Determine (a) the thermal efficiency of the cycle and (b) the fraction of flow extracted where bleeding occurs. (c)

What-if Scenario: What would the answer in (b) be if the bleeding pressure were increased to 1.5 MPa? [Edit Problem] [TEST Solution] Answers: (a) 45.7%, (b) 0.2199, (c) 0.2327 Image of a steam power plant under construction

9-1-28 [regen-5MPa] A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 5 MPa, 450 o C and is condensed in the condenser at 15 kPa. Steam is extracted from the turbine at a pressure of 0.4 MPa and enters the open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Determine (a) the thermal efficiency of the cycle and (b) the net work output per kilogram of steam flowing through the boiler. [Edit Problem] [Manual Solution] [TEST Solution] Answers: (a) 37.8%, (b) 1025 kJ/kg

9-1-29 [regen-8MPa] A regenerative vapor power cycle has two turbine stages with steam entering the first turbine stage at 8 MPa, 550 o C and expanding to 700 kPa, where some of the steam is extracted and diverted to the open feedwater heater operating at 700 kPa. The remaining steam expands through the second turbine stage to the condenser at a pressure of 7 kPa. Saturated liquid exits the open feedwater heater at 700 kPa. Each turbine stage has an isentropic efficiency of 88% and each pump has an isentropic efficiency of 80%. Determine (a) the thermal efficiency of the cycle, (b) the net power developed and (c) the fraction of flow extracted where bleeding occurs. (d) What-if Scenario: What would the net power developed be if the mass flow rate of steam entering the first stage of turbine were 170 kg/s? [Edit Problem] [TEST Solution] Answers: (a) 39.4%, (b) 1.1 MW, (c) 0.1932 kg/s, (d) 188.6 MW

Anim. 9-1-29(click)

9-1-30 [regen-12MPa] A regenerative vapor power cycle has two turbine stages with steam entering the first turbine stage at 12 MPa, 600 o C and expands to 1 MPa, where some of the steam is extracted and diverted to the open feedwater heater operating at 1 MPa. The remaining steam expands through the second turbine stage to a condenser at pressure of 6 kPa. Saturated liquid exits the open feedwater heater at 6 kPa. Each turbine stage and pump has an isentropic efficiency of 80%. The mass flow rate into the first turbine stage is 100 kg/s. Determine (a) the thermal efficiency of the cycle, (b) the net power developed and (c) the heat transfer to the steam in the steam generator. (d) What-if Scenario: What would the net power developed be if the feedwater pressure were 1.4 MPa? [Edit Problem] [TEST Solution] Answers: (a) 38.8%, (b) 109.8 MW, (c) 282.9 kW, (d) 107 MW

9-1-31 [regen-10MPa] A power plant operates on a regenerative vapor power cycle with one closed feedwater heater. Steam enters the first turbine stage at 10 MPa, 500 o C and expands to 1 MPa, where some of the steam is extracted and diverted to a closed feedwater heater. Condensate exiting the feedwater heater as saturated liquid at 1 MPa passes

through a trap into the condenser. The feedwater exits the heater at 10 MPa with a temperature of 175 o C. The condenser pressure is 6 kPa. The mass flow rate into the first stage turbine is 270 kg/s. For isentropic processes in each turbine stage and the pump, determine (a) the mass flow rate of steam extracted from the turbine, (b) the thermal efficiency of the cycle and (c) the net power developed. [Edit Problem] [TEST Solution] Answers: (a) 78.83 kg/s, (b) 42.44%, (b) 300.5 MW

Fig. 9-1-31

9-1-32 [regen-noTrap] Repeat problem 9-1-31 above by replacing the trap with a pump and a mixing chamber as shown in the schematic below. [Edit Problem] [TEST Solution] Answers: (a) 61.01 kg/s, (b) 44.42%, (c) 313.9 MW

Fig. 9-1-32

9-1-33 [regen-7MPa] A power plant operates on a regenerative vapor power cycle with one closed feedwater heater. Steam enters the first turbine stage at 7 MPa, 550 o C and expands to 700 kPa, where some of the steam is extracted and diverted to a closed feedwater heater. Condensate exiting the feedwater heater as saturated liquid at 700 kPa passes through a trap into the condenser. The feedwater exits the heater at 7 MPa with a temperature of 175 o C. The condenser pressure is 8 kPa. If the power developed is 100 MW, determine (a) the thermal efficiency of the cycle and (b) the mass flow rate into the first stage turbine. (c) What-if Scenario: What would the thermal efficiency be if the extraction pressure were 600 kPa? [Edit Problem] [TEST Solution] Answers: (a) 41.9%, (b) 86 kg/s, (c) 42.2%

9-1-34 [regen-520C] A power plant operates on a regenerative vapor power cycle with one closed feedwater heater. Steam enters the first turbine stage at 12 MPa, 520 o C and expands to 1200 kPa, where some of the steam is extracted and diverted to a closed feedwater heater. Condensate exiting the feedwater heater as saturated liquid at 120 kPa passes through a trap into the condenser. The feedwater exits the heater at 7 MPa with a temperature of 170 o C. The condenser pressure is 12 kPa. If the mass flow rate into first

stage of turbine is 300 kg/s and each turbine stage has an isentropic efficiency of 80%, determine (a) the thermal efficiency of the cycle and (b) the net power developed. (c) What-if Scenario: What would the net power developed be if the condenser pressure were 9 kPa? [Edit Problem] [TEST Solution] Answers: (a) 34.5%, (b) 276.3 MW, (c) 272.9 MW

9-1-35 [reheatGen-100MW] A power plant operates on an ideal reheat-regenerative Rankine cycle and has a net power output of 100 MW. Steam enters the high pressure turbine stage at 12 MPa, 550 o C and leaves at 0.9 MPa. Some steam is extracted at 0.9 MPa to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500 o C and is expanded in the low pressure turbine to the condenser at a pressure of 8 kPa. Determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of steam through the boiler. (c) What-if Scenario: What would the thermal efficiency be if the steam entered the turbine at 15 MPa? [Edit Problem] [TEST Solution] Answers: (a) 45.6%, (b) 67.2 kg/s, (c) 44.9 %

Fig. 9-1-35

9-1-36 [reheatGen-closedFWH] Repeat problem 9-1-35 , but replace the open feedwater heater with closed feedwater heater. Assume that the feedwater leaves the heater at the condensation temperature of the extracted steam (T4) and that the extracted steam leaves the heater at state-10 as a saturated liquid before it is pumped to the line carrying the feedwater. Determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of steam through the boiler. [Edit Problem] [TEST Solution] Answers: (a) 45.93%, (b) 67.02 kg/s

Fig. 9-1-36

9-1-37 [reheatGen-12MPa] A steam power plant operates on a reheat-regenerative Rankine cycle with a closed feedwater heater. Steam enters the turbine at 12 MPa, 500 o C at a rate of 25 kg/s and is condensed in the condenser at a pressure of 20 kPa. Steam is reheated at 5 MPa to 500 o C. Steam at a rate of 5 kg/s is extracted from the low pressure turbine at 1.2 MPa, and is completely condensed in the closed feedwater heater, and pumped to 12 MPa before it mixes with the feedwater at the same pressure. Assuming an isentropic efficiency of 88% for both the turbine and the pump, determine (a) the temperature at the inlet of the closed feedwater heater, (b) the thermal efficiency of the cycle and (c) the net power output. [Edit Problem] [TEST Solution] Answers: (a) 309 o C, (b) 38.2%, (c) 27 MW,

Fig. 9-1-37

9-1-38 [reheatGen-10MPa] A steam power plant operates on an ideal reheat-regenerative Rankine with one reheat and two open feedwater heaters. Steam enters the high pressure turbine at 10 MPa, 600 o C and leaves the low pressure turbine at 7 kPa. Steam is extracted from the turbine at 2 MPa and 275 kPa, and it is reheated to 540 o C at a pressure of 1 MPa. Water leaves both feedwater heaters as saturated liquid. Heat is transferred to the steam in the boiler at a rate of 6 MW. Determine (a) the mass flow rate of steam through the boiler, (b) the net power output and (c) the thermal efficiency of the cycle. [Edit Problem] Answers: (a) 1.9 kg/s, (b) 2.9 MW, (c) 47.6%

Fig. 9-1-38

9-1-39 [reheatGen-500C] Consider a reheat-regenerative vapor power cycle with two feedwater heaters, a closed feedwater heater and an open feedwater heater. Steam enters the first turbine at 10 MPa, 500 o C and expands to 0.8 MPa. The steam is reheated to 440 o C before entering the second turbine, where it expands to the condenser at a pressure of 0.007 MPa. Steam is extracted from the first turbine at 2 MPa and fed to the closed

feedwater heater. Feedwater leaves the closed heater at 205 o C, 10 MPa and condensate exits as saturated liquid at 2 MPa. The condensate is trapped into the open feedwater heater. Steam extracted from second turbine at 0.3 MPa is also fed into the open feedwater heater, which operates at 0.3 MPa. The steam exiting the open feedwater heater is saturated liquid at 0.3 MPa. The net power output of the cycle is 100 MW. There is no stray heat transfer from any component to its surroundings. If the working fluid experiences no irreversibilities as it passes through the turbines, pumps, steam generator, reheater and condenser, determine (a) the thermal efficiency of the cycle and (b) the mass flow rate of steam entering the first turbine. [Edit Problem] [TEST Solution] Answers: (a) 44.6%, (b) 75 kg/s

Anim. 9-1-39(click) Section-2: Cogeneration, Combined and Binary Cycles

9-2-1 [water-320C] Water is the working fluid in a cogeneration cycle that generates electricity and provides heat for campus buildings. Steam at 2.5 MPa, 320 o C, with a mass flow rate of 1 kg/s, expands through a two-stage turbine. Steam at 0.2 MPa is extracted with a mass flow rate of 0.3 kg/s between the two stages and provided for heating. The remaining steam expands through the second stage to the condenser at a pressure of 6 kPa. The condensate returns from the campus buildings at 0.1 MPa, 60 o C and passes through a trap into the condenser. Each turbine stage has an isentropic efficiency of 80%. Determine (a) the net heat transfer rate to the working fluid passing through the steam generator, (b) the net power developed and (c) the rate of heat transfer for building heating. (d) What-if Scenario: What would the rate of heat transfer be if the inlet [Edit Problem] [TEST Solution] conditions at the turbine were 3 MPa and 400 o C? Answers: (a) 2902 kW, (b) 684 kW, (c) 719 kW, (d) 748.6 kW

Anim. 9-2-1(click)

9-2-2 [water-9MPa] Water is the working fluid in a cogeneration cycle. Steam generator provides 280 kg/s of steam at 9 MPa, 500 o C, of which 110 kg/s is extracted between the first and second stages at 1.5 MPa and diverted to a process heating load. Condensate returns from the process heating load at 1 MPa, 120 o C and is mixed with the liquid exiting the lower pressure pump at 1 MPa. The entire flow is then pumped to the steam generator pressure. Saturated liquid at 8 kPa leaves the condenser. The turbine stages and pumps operate with isentropic efficiencies of 90% and 80%, respectively. Determine (a) the net heat transfer rate to the working fluid passing through the steam generator, (b) the net power developed and (c) the heating load. [Edit Problem] [TEST Solution] Answers: (a) 859.9 MW, (b) 247.6 MW, (c) 268.6 MW

Anim. 9-2-2(click)

9-2-3 [food-550kPa] A large food processing plant requires 3.5 kg/s of saturated or slightly superheated steam at 550 kPa, which is extracted from the turbine of a cogeneration plant. The boiler generates steam at 7 MPa, 540 o C at a rate of 9 kg/s, and the condenser pressure is 14 kPa. Steam leaves the process heater as saturated liquid. It is then mixed with the feedwater at the same pressure and this mixture is pumped to the boiler pressure. Assuming both the pumps and the turbine have adiabatic efficiencies of 86%, determine (a) the net heat transfer rate to the working fluid passing through the steam generator and (b) the power output of the cogeneration plant. (c) What-if Scenario: What would the power output be if the efficiencies of both the pumps and the turbine were 100%? [Edit Problem] [TEST Solution] Answers: (a) 27.9 MW, (b) 8.18 MW, (c) 9.3 MW

9-2-4 [steam-8MPa] Consider a cogeneration plant. Steam enters the turbine at 8 MPa and 600 o C. 20% of the steam is extracted before it enters the turbine and 60% of the steam is extracted from the turbine at 500 kPa for process heating . The remaining steam continues to expand to 6 kPa. Steam is then condensed at constant pressure and pumped to the boiler pressure of 8 MPa. Steam leaves the process heater as a saturated liquid at 500 kPa. The mass flow rate of steam through the boiler is 20 kg/s.Determine (a) the rate of process heat supply and (b) the net power developed. (c) What-if Scenario: What would the net power developed be if no process heat were to be supplied? [Edit Problem] [TEST Solution] Answers: (a) 33.1 MW, (b) 17.02 MW, (c) 29.4 MW

Anim. 9-2-4(click)

9-2-5 [steam-maxRate] Repeat problem 9-2-4 to determine (a) the maximum rate at which process heat can be supplied. [Edit Problem] [TEST Solution] Answers: (a) 59.8 MW

9-2-6 [steam-4MPa] Steam is generated in the boiler of a cogeneration plant at 4 MPa and 480 o C at a rate of 7 kg/s. The plant is to produce power while meeting the process steam requirements for a certain industrial application. One-third of the steam leaving the boiler is throttled to a pressure of 820 kPa and is routed to the process heater. The rest of the steam is expanded in an isentropic turbine to a pressure of 820 kPa and is also routed to the process heater. Steam leaves the process heater as saturated liquid. Determine (a) the net power produced and (b) the rate of process heat supply. (c) What-if Scenario: What would the net power produced be if one-half instead of one-third of the steam leaving the boiler were throttled? [Edit Problem] [TEST Solution] Answers: (a) 2.06 MW, (b) 16.6 MW, (c) 17.1 MW

Anim. 9-2-6(click)

9-2-7 [steam-5MPa] Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 5 MPa, 450 o C and expands to a pressure of 0.6 MPa. At this pressure 65% of the steam is extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is used to heat the feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as saturated liquid at 0.6 MPa. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines and the pumps to be isentropic,(a) determine the mass flow rate of the steam through the boiler for a net power output of 15 MW. (b) What-if Scenario: What would the mass flow rate of steam be if only 50% of steam were extracted from the turbine? [Edit Problem] [TEST Solution] Answers: (a) 20.1 kg/s, (b) 17.87 kg/s

Anim. 9-2-7(click)

9-2-8 [regen-7MPa] Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 7 MPa, 440 o C at a rate of 20 kg/s and expands to a pressure of 0.4 MPa. At this pressure 60% of the steam is extracted from the turbine, and the remainder expands to 10 kPa. Part of the extracted steam is used to heat the feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as a saturated liquid at 0.4 MPa. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines and the pumps to be isentropic, determine (a) the total power output of the turbine, (b) the mass flow rate of the steam through the process heater, (c) the rate of heat supply from the process heater per unit mass of steam passing through it and (d) the rate of heat transfer to the steam boiler. [Edit Problem] [TEST Solution] Answers: (a) 17 MW, (b) 10.3 kg/s, (c) 2000 kJ/kg, (d) 52.9 MW

9-2-9 [gasTurbine-pr15] The gas-turbine portion of a combined gas-steam power plant has a pressure ratio of 15. Air enters the compressor at 300 K at a rate of 13 kg/s and is heated to 1500 K in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to 400 o C at 10 MPa in a heat exchanger. The combustion gases leave the heat exchanger at 420 K. The steam leaving the turbine is condensed at 15 kPa. Assuming all the compression and expansion processes to be isentropic,determine (a) the mass flow rates of steam, (b) the net power output and (c) the thermal efficiency of the combined cycle. (d) What-if Scenario: What would the thermal efficiency be if the compression ratio were increased to 17? [Edit Problem] [TEST Solution] Answers: (a) 1.6 kg/s, (b) 8.3 MW, (c) 64.7%, (d) 65.6%

Anim. 9-2-9(click)

9-2-10 [gasSteam-600MW] Consider a combined gas-steam power plant that has a net power output of 600 MW. The pressure ratio of the gas turbine cycle is 16. Air enters the compressor at 300 K and the turbine at 1600 K. The combustion gases leaving the gas turbine are used to heat the steam to 400 o C at 10 MPa in a heat exchanger. The combustion gases leave the heat exchanger at 400 K. An open feedwater heater incorporated with the

steam cycle operates at a pressure of 0.6 MPa. The condenser pressure is 15 kPa. Assuming all the compression and expansion processes to be isentropic,determine (a) the mass flow rate of steam and (b) the thermal efficiency of the combined cycle. (c) What-if Scenario: What would the thermal efficiency be if the compression ratio were increased to 17? [Edit Problem] [TEST Solution] Answers: (a) 811 kg/s, (b) 67.4%, (c) 68.3%

Anim. 9-2-10(click)

9-2-11 [gasSteam-100pct] Repeat problem 9-2-10 assuming isentropic efficiencies of 100% for the pump, 82% for the compressor, 86% for the gas and steam turbines. Determine (a) the mass flow rate of steam and (b) the thermal efficiency of the combined cycle. [Edit Problem] [TEST Solution] Answers: (a) 1090 kg/s, (b) 54.1%

9-2-12 [gasVapor-15MW] A combined gas turbine-vapor power plant has a net power output of 15 MW. Air enters the compressor of the gas turbine at 100 kPa, 290 K and is compressed to 1100 kPa. The isentropic efficiency of the compressor is 80%. The conditions at the inlet to the turbine are 1100 kPa and 1400 K. Air expands through the turbine, that has an isentropic efficiency of 88%, to a pressure of 100 kPa. Air then passes through the interconnecting heat exchanger, and is finally discharged at 420 K. Steam enters the turbine of the vapor power cycle at 8 MPa, 390 o C and expands to the condenser at a pressure of 8 kPa. Water enters the pump as saturated liquid at 8 kPa. The turbine and pump have isentropic efficiencies of 90% and 80%, respectively. Determine (a) the thermal efficiency of the combined cycle, the mass flow rates of (b) air and (c) water, and (d) the rate of heat transfer to the combined cycle. [Edit Problem] [TEST Solution] Answers: (a) 50.4%, (b) 34.1 kg/s, (c) 5.3 kg/s, (d) 29.7 kW

Anim. 9-2-12(click)

9-2-13 [topping-101kPa] A simple gas turbine is the topping cycle for a simple vapor power cycle. Air enters the compressor of the gas turbine at 101 kPa, 15 o C and mass flow rate of 23 kg/s. The compressor pressure ratio is 10 and the turbine inlet temperature is 1100 o C. The compressor and turbine have an isentropic efficiency of 85%. Air leaves the interconnecting heat exchanger at 200 o C and 101 kPa. Steam enters the turbine of the vapor power cycle at 7 MPa, 480 o C and expands to the condenser pressure of 7 kPa. Water enters the pump as saturated liquid at 7 kPa. The turbine and pump have isentropic efficiencies of 90% and 80%, respectively. Determine (a) the thermal efficiency of the combined cycle, (b) the mass flow rates of water and (c) the net power output. [Edit Problem] [TEST Solution] Answers: (a) 47.8%, (b) 3.2 kg/s, (c) 9.6 MW

9-2-14 [helium-350K] Consider a combined cycle power plant using helium and water as the working fluids. Helium enters the compressor of the gas turbine at 1.4 MPa, 350 K and is compressed to 5.5 MPa. The isentropic efficiency of the compressor is 80%. The conditions at the inlet to the turbine are 5.5 MPa and 760 o C. Helium expands through the turbine to a pressure of 1.4 MPa. The turbine has an isentropic efficiency of 80%. The mass flow rate of the gas is 100 kg/s. Saturated vapor at 8 MPa exits the heat exchanger which is superheated to 425 o C before it enters the turbine of the vapor power cycle, and expands to the condenser at a pressure of 7 kPa. The steam exits the turbine at a quality of 0.9. Water enters the pump as saturated liquid at 7 kPa. Determine (a) the thermal efficiency of the combined cycle, (b) the mass flow rates of steam and (c) the net power developed. (d) What-if Scenario: What would the thermal efficiency be if air were used as working fluid for the gas phase? [Edit Problem] [TEST Solution] Answers: (a) 33.2%, (b) 67.2 kg/s, (c) 73 MW, (d) 36.1%

Anim. 9-2-14(click)

9-2-15 [ammonia-6MPa] Steam and ammonia are the working fluids in a binary vapor power cycle consisting of two ideal Rankine cycles. The heat rejected from the steam cycle is provided to the ammonia cycle. In steam cycle, steam at 6 MPa, 650 o C enters the turbine and exits at 60 o C. Saturated liquid at 60 o C enters the pump and is pumped to the steam generator pressure. Saturated vapor of ammonia enters the turbine at 50 o C and exits at 1 MPa which enters the condenser and condenses to saturated liquid. The saturated liquid is then pumped through the heat exchanger. The power output of the binary cycle is 25 MW. Determine (a) the mass flow rates of steam and ammonia, (b) the power outputs of the steam and ammonia turbines, (c) the rate of heat addition to the cycle and (d) the thermal efficiency. [Edit Problem] [TEST Solution] Answers: (a) 16.4 kg/s, 30.14 kg/s, (b) 22.49 MW, 2.66 MW, (c) 57.72 MW, (d) 43.32%

Fig. 9-2-15

9-2-16 [r134a-4MPa] Water and refrigerant R-134a are the working fluids in a binary cycle used for cogeneration of power and process steam. In the steam cycle, superheated vapor enters the turbine with a mass flow rate of 5 kg/s at 4 MPa, 470 o C and expands isentropically to 150 kPa. Half of the flow is extracted at 150 kPa and is used for industrial process heating. The rest of the stream passes through a heat exchanger, which serves as the boiler for the refrigerant cycle and the condenser of the steam cycle. The condensate leaves the heat exchanger as saturated liquid at 100 kPa, which is combined with the return flow from the process, at 100 kPa and 65 o C, before being pumped isentropically to the steam generator pressure. Refrigerant 134a is in an ideal Rankine cycle with refrigerant entering the turbine at 1.5 MPa, 101 o C and saturated liquid leaving the condenser at 800 kPa. Determine (a) the rate of heat transfer to the working fluid passing through the steam generator of the steam cycle, (b) the net power output of the binary cycle, (c) the mass flow rate of the refrigerant and (d) the rate of heat transfer to the industrial process. (e) What-if Scenario: What would the mass flow rate be if refrigerant R-12 were used instead of R-134a? [Edit Problem] [TEST Solution] Answers: (a) 13.29 MW, (b) 2.34 MW, (c) 23.35 kg/s, (d) 5.84 MW, (e) 31.1 kg/s

Fig. 9-2-16

9-2-17 [geothermal-200C] Geothermal resource exits as saturated liquid at 200 o C. The geothermal liquid is withdrawn from a production well at a rate of 200 kg/s, and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process, where the resulting vapor is separated from the liquid in a separator and is directed to the turbine. Steam leaves the turbine at 12 kPa with a moisture content of 14 percent and enters the condenser, where it is condensed and routed to a reinjection well, along with the liquid coming from the separator. Determine (a) the mass flow rate of steam through the turbine and (b) the power output of the turbine. [Edit Problem] [TEST Solution] Answers: (a) 20.1 kg/s, (b) 9.8 MW

Fig. 9-2-17 Section-3: Exergy Analysis of Vapor Power, Cogeneration, and Binary Cycles

9-3-1 [rankine-4MPa] Consider a steam power plant operating on the simple ideal Rankine cycle. Steam enters the turbine at 4 MPa, 400 o C and is condensed in the condenser at a pressure of 100 kPa. The mass flow rate is 10 kg/s. If the boiler receives heat from a source at 1200 o C and the condenser rejects heat to a reservoir at 25 o C, determine (a) the thermal efficiency of the cycle, (b) the exergetic efficiency of the cycle and (c) draw an exergy flow diagram for the cycle. Assume the atmospheric conditions to be 100 kPa and [Edit Problem] [TEST Solution] 25 o C. Answers: (a) 27%, (b) 33.87%

Anim. 9-3-1(click)

9-3-2 [rankine-10MPa] Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 10 MPa and saturated liquid exits the condenser at a pressure of 0.01 MPa. The net power output of the cycle is 150 MW. The turbine and the pump both have an isentropic efficiency of 85%. If the boiler receives heat from a source at 1200 o C and the condenser rejects heat to a reservoir at 25 o C, (a) identify the device of maximum exergy destruction, (b) determine the exergetic efficiency of the cycle and (c) draw an exergy flow diagram for the cycle. Assume the atmospheric conditions to be 100 kPa and 25 o C. [Edit Problem] [TEST Solution] Answers: (b) 39.52%

Anim. 9-3-2(click)

9-3-3 [regen-9MPa] In a steam power plant operating on the ideal regenerative Rankine cycle with one open feedwater heater, steam enters the turbine at 9 MPa, 480 o C and is condensed in the condenser at a pressure of 7 kPa. Bleeding from the turbine to the FWH occurs at 0.7 MPa. The net power output of the cycle is 100 MW. The boiler receives heat from a source at 1200 o C and the condenser rejects heat to atmosphere at 100 kPa, 25 o C. (a) Perform an exergy inventory and draw an exergy flow diagram for the cycle. Determine (b) the thermal efficiency and (c) exergetic efficiency of the cycle. [Edit Problem] [TEST Solution] Answers: (b) 43.37%, (c) 54.38%

Anim. 9-3-3(click)

9-3-4 [regen-noBled] Repeat problem 9-3-3 , assuming no steam is bled from the turbine for regeneration. [Edit Problem] [TEST Solution] Answers: (b) 40.47%, (c) 50.74%

9-3-5 [cogen-320C] Water is the working fluid in a cogeneration cycle that generates electricity and provides heat for campus buildings. Steam at 2.5 MPa, 320 o C and a mass flow rate of 1 kg/s, expands through a two-stage turbine. Steam at 0.2 MPa with a mass flow rate of 0.3 kg/s is extracted between the two stages and provided for heating. The remaining steam expands through the second stage to the condenser at a pressure of 6 kPa. The condensate returns from the campus buildings at 0.1 MPa, 60 o C and passes through a trap into the condenser. Each turbine stage has an isentropic efficiency of 80%. Heat addition to the boiler takes place from a source at 1200 o C, the building is maintained at 50 o C, and the atmospheric conditions are 100 kPa, 20 o C. (a) Perform an exergy analysis and draw an exergy flow diagram for the system. (b) Define and evaluate the exergetic efficiency of the system. [Edit Problem] [TEST Solution] Answers: (b) 32.3%

Anim. 9-3-5(click) Version No: 37; Last Updated: 2010-10-31 11:03:40

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