Section-1: Basic and Modified Brayton Cycles
8-1-1 [compressor-pr12] Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 25 o C, with a volumetric flow rate of 8 m 3 /s. The compressor pressure ratio is 12. The turbine inlet temperature is 1100 o C. Determine (a) the thermal efficiency, (b) net power output and (c) back work ratio. Use the PG model for air. (d) What-if Scenario: What would the answers be if the IG model were used? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 50.9%, (b) 3657 kW, (c) 44.2%, (d) 48.2%, 3961 kW, 42%
Anim. 8-1-1(click)
8-1-2 [turbine-1000C] A stationary power plant operating on an ideal Brayton cycle has a pressure ratio of 7. The gas temperature is 25 o C at the compressor inlet and 1000 o C at the turbine inlet. Utilizing the air standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) back work ratio and (c) the thermal efficiency. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 520 K, 730 K, (b) 40.8%, (c) 42.7%
8-1-3 [tmax-1225C] In an air standard Brayton cycle the air enters the compressor at 0.1 MPa, 20 o C. The pressure leaving the compressor is 1 MPa, and the maximum temperature in the cycle is 1225 o C. Determine (a) the compressor work, (b) turbine work and (c) the cycle efficiency. Use the PG model. (d) What-if Scenario: What would the answers be if the compressor exit pressure were 1.5 Mpa? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 274.14 kJ/kg, (b) 725.19 kJ/kg, (c) 48.2% (d) 344 kJ/kg, 810.4 kJ/kg, 53.9%
Anim. 8-1-3(click)
8-1-4 [compressor-305K] Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 305 K with a volumetric flow rate of 5 m 3 /s. The compressor pressure ratio is 10. The turbine inlet temperature is 1000 K. Determine (a) the thermal efficiency, (b) net power output and (c) back work ratio. Use the PG model for air. (d) What-if Scenario: What would the net power output be if the turbine inlet temperature were 1500 K. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 48.23%, (b) 1135.8 kW, (c) 58.9%, (d) 2518.36 kW
8-1-5 [heat-8000kW] A gas turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 1 MPa and 1000 K and leaves at 125 kPa, 610 K. Heat is rejected to the surroundings at a rate of 8000 kW and air flow rate is 25 kg/s. Assuming a compressor efficiency of 80%, determine (a) the net power output. Use the PG model for air. (b) What-if Scenario: What would the net power output be if the compressor efficiency dropped to 75%? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 2367 kW, (b) 1872 kW
Anim. 8-1-5(click)
8-1-6 [turbine-90pct] Repeat problem 8-1-4 above assuming a compressor efficiency of 80% and a turbine efficiency of 90%, and determine (a) back work ratio, (b) the thermal efficiency and (c) the turbine exit temperature. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 81.8%, (b) 23.2%, (c) 565.85 K.
Anim. 8-1-6(click)
8-1-7 [turbine-85pct] In a air standard Brayton cycle the air enters the compressor at 0.1 MPa, 20 o C. The pressure leaving the compressor is 1 MPa, and the maximum temperature in the cycle is 1225 o C. Assume a compressor efficiency of 80%, a turbine efficiency of 85% and a pressure drop between the compressor and turbine of 25 kPa. Determine (a) the compressor work, (b) the turbine work and (c) the cycle efficiency. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 342.6 kW (b) 611.6 kW, (c) 31%
8-1-8 [compressor-195kPa] Air enters the compressor of an ideal air standard Brayton cycle at 195 kPa, 290 K, with a volumetric flow rate of 6 m 3 /s. The compressor pressure ratio is 9. The turbine inlet temperature is 1400 K. The compressor has an efficiency of 90% and the turbine has an efficiency of 75%. Determine (a) the thermal efficiency, (b) net power output and (c) back work ratio. Use the PG model for air. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 25.12%, (b) 2935.2 kW, (c) 57.5%
8-1-9 [heat-6800kW] A gas turbine power plant operates on a simple Brayton cycle with air as the working fluid. Air enters the turbine at 800 kPa and 1200 K; it leaves the turbine at 100 kPa and 750 K. Heat is rejected to the surroundings at a rate of 6800 kW, and air flows through the cycle at a rate of 20 kg/s.Assuming a compressor efficiency of 80%, determine (a) net power output of the plant. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 650.3 kW
8-1-10 [power-25MW] Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 310 K, and a turbine inlet temperature of 900 K. Determine (a) the required mass flow rate of air for a net power of 25 MW, assuming both the compressor and the turbine have an isentropic efficiency of 90%. Use the PG model. (b) What-if Scenario: What would the mass flow rate be if both compressor and the turbine had 100% efficiency? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 450 kg/s, (b) 183 kg/s
8-1-11 [power-10MW] A gas turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 10 MW of power. The minimum and maximum temperatures in the cycle are 300 K and 1100 K, and the pressure of air at the compressor exit is 9 times the value at the compressor inlet. Assuming an adiabatic efficiency of 80% for the compressor and 90% for the turbine, determine (a) the mass flow rate of air through the cycle. Use the PG model. (b) What-if Scenario: What would the mass flow rate be if the IG model were used? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 74.4 kg/s, (b) 66.7 kg/s.
8-1-12 [turbine-88pct] Air enters the compressor of a simple gas turbine at 100 kPa, 25 o C, with a volumetric flow rate of 6 m 3 /s. The compressor pressure ratio is 10 and its isentropic efficiency is 80%. The turbine inlet the pressure is 100 kPa temperature is 1000 o C. The turbine has an isentropic efficiency of 88% and the exit pressure is 100 kPa. On the basis of air standard analysis using the PG model, determine (a) the thermal efficiency of the cycle, (b) net power developed, in kW. (c) What-if Scenario: What would the answers be if the inlet temperature increased to 50 o C? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 30.8%, (b) 1359 kW, (c) 28.6%, 1064 kW
8-1-13 [heat-1000kJkg] Air enters the compressor of a simple gas turbine at 95 kPa, 310 K, where it is compressed to 800 kPa. Heat is transferred to air in the amount of 1000 kJ/kg before it enters the turbine. For a turbine efficiency of 90%, determine (a) the thermal efficiency of the cycle, (b) the fraction of turbine work output used to drive the compressor. Use the PG model for air. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 36.69%, (b) 44.23%
8-1-14 [reheat-1000K] Air enters the compressor of a simple gas turbine at 0.1 MPa, 300 K. The pressure ratio is 9 and the maximum temperature is 1000 K. The turbine process is divided into two stages each with a pressure ratio of 3, with intermediate reheating to 1000 K. Determine (a) the cycle efficiency and (b) net output. Use the PG model. (c) What-if Scenario: What would the answers be if the reheat were eliminated? [Edit Problem] [TEST Solution]
Answers: (a) 39.15%, (b) 277.8 kJ/kg, (c) 46.65%, 204.8 kJ/kg
Anim. 8-1-14(click)
8-1-15 [reheat-1kg] Repeat problem 8-1-14 for the net output per kg of air, assuming the pressure ratio of the first stage turbine before reheat to be (a) 7, (b) 5, (c) 3, (d) 2. (e) Use a T-s diagram to explain why the output increases and then decreases. [Edit Problem] [TEST Solution]
Answers: (a) 234.6 kJ/kg, (b) 262.2 kJ/kg, (c) 277.8 kJ/kg, (d) 268.0 kJ/kg
8-1-16 [regen-70pct] Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 290 K, with a mass flow rate of 6 kg/s. The compressor pressure ratio is 10. The turbine inlet temperature is 1500 K. If a regenerator with an effectiveness of 70% is incorporated in the cycle, determine (a) the thermal efficiency of the cycle. Use the PG model for air. (b) What-if Scenario: What would the thermal efficiency be if the regenerator effectiveness increased to 90% ? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 57.50%, (b) 60.83%
Anim. 8-1-16(click)
8-1-18 [compressor-82pct] A Brayton cycle with regeneration and air at 100 kPa as the working fluid operates on a pressure ratio of 8. The minimum and maximum temperatures of the cycle are 300 and 1200 K. The adiabatic efficiencies of the turbine and the compressor are 80% and 82% respectively. The regenerator effectiveness is 65%. Determine (a) the thermal efficiency and (b) net power output. Use the PG model. (c) What-if Scenario: What would the thermal efficiency be if the regenerator effectiveness increased to 75%? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 27.12%, (b) 133.5 kW, (c) 28.11%
8-1-19 [turbine-100hp] A 100-hp, regenerative, Brayton-cycle gas turbine operates between a source at 840 o C and the reference atmosphere at 21 o C. Air enters the compressor at 21 o C, 101 kPa. The air is then compressed to 345 kPa and then heated to 840 o C. Part of this heating is accomplished in a regenerator whose effectiveness is 90%. Determine (a) the thermal efficiency of the cycle, (b) work done by compressor and (c) work done by turbine. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 56.2%, (b) 44.9 kW, (c) 119.7 kW
8-1-21 [turbine-1200K] Air enters the compressor of a regenerative gas turbine engine at 100 kPa, 290 K, where it is compressed to 750 kPa and 550 K. The regenerator has an effectiveness of 70%, and the air enters the turbine at 1200 K. For a turbine efficiency of 80%, determine (a) the amount of heat transfer in the regenerator and (b) the thermal efficiency of the cycle. Assume variable specific heats of air. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 183 kJ/kg, (b) 32.4%
8-1-22 [intercooler-350kPa] Air is compressed from 100 kPa, 310 K to 1000 kPa in a two stage compressor with intercooling between stages. The intercooler pressure is 350 kPa. The air is cooled back to 310 K in the intercooler before entering the second compressor stage. Each compressor stage is isentropic. Determine (a) the temperature at the exit of the second compressor stage and (b) the total compressor work in kJ/kg. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 417.3 K, (b) 242.6 kJ/kg
Fig. 8-1-22
8-1-23 [reheat-300kPa] Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 25 o C with a volumetric flow rate of 8 m 3 /s and is compressed to 1000 kPa. The temperature at the inlet to the first turbine stage is 1000 o C. The expansion takes place isentropically in two stages, with reheat to 1000 o C between the stages at a constant pressure of 300 kPa. If a regenerator having an effectiveness of 100% is incorporated in the cycle, determine (a) the thermal efficiency of the cycle. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 62.1%
Anim. 8-1-23(click)
8-1-24 [turbine-pr2] Consider an ideal gas turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and the turbine is 2. Air enters each stage of the compressor at 310 K and each stage of the turbine at 1100 K. Determine (a) the thermal efficiency of the cycle and (b) back work ratio. Use the IG model. (c) What-if Scenario: What would the thermal efficiency and BWR be if the pressure ratio across each stage of the compressor and the turbine were 4 ? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 27%, (b) 34%, (c) 40.7%, 40.9%
Anim. 8-1-24(click)
8-1-25 [regen-80pct] Repeat problem 8-1-24 assuming a regenerator with 80% effectiveness is added at the end of the last compressor. Determine (a) the thermal efficiency of the cycle and (b) back work ratio. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 30.57%, (b) 34%
Anim. 8-1-25(click)
8-1-26 [power-50MW] Consider a regenerative gas turbine power plant with two stages of compression and two stages of expansion. The overall pressure ratio of the cycle is 9. Air enters each stage of compressor at 290 K and each stage of turbine at 1400 K, the regenerator has an effectiveness of 100%. Determine (a) the minimum mass flow rate of air needed to develop a net power output of 50 MW. Use the IG model. (b) What-if Scenario: What would the mass flow rate be if argon were used as the working fluid ? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 89.2 kg/s, (b) 142.2 kg/s
8-1-27 [compressor-80pct] Repeat 8-1-24 assuming an efficiency of 80% for each compressor stage and an efficiency of 85% for each turbine stage. Determine (a) the thermal efficiency of the cycle and (b) back work ratio. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 18.2%, (b) 49.9%
Anim. 8-1-27(click)
8-1-28 [turbine-1100K] Repeat problem 8-1-24 assuming an efficiency of 80% for each compressor stage and an efficiency of 85% for each turbine stage, and a regenerator with 80% effectiveness. Determine (a) the thermal efficiency of the cycle and (b) the back work ratio. [Edit Problem] [TEST Solution]
Answers: (a) 37%, (b) 49.9%
Anim. 8-1-28(click)
8-1-29 [compressor-8kgs] A regenerative gas turbine with intercooling and reheat operates at steady state. Air enters the compressor at 100 kPa, 300 K with a mass flow rate of 8 kg/s. The pressure ratio across the two stage compressor and two stage turbine is 12. The intercooler and reheater each operates at 300 kPa. At the inlets to the turbine stages the temperature is 1500 K. The temperature at the inlet to the second compressor stage is 300 K. The efficiency of each compressor is 85%, and turbine stages is 80%. The regenerator effectiveness is 75%. Determine (a) the thermal efficiency, (b) the back work ratio and (c) the net power developed. Use the IG model. [Edit Problem] [TEST Solution]
Answers: (a) 46%, (b) 40.9%, (c) 3489.4 kW
8-1-30 [compressor-50kgs] Air enters steadily the first compressor of the gas turbine at 100 kPa and 300 K with a mass flow rate of 50 kg/s. The pressure ratio across the two-stage compressor and turbine is 15. The intercooler and reheater each operates at an intermediate pressure given by the square root of the product of the first compressor and turbine inlet pressures. The inlet temperature of each turbine is 1500 K and that of the second compressor is 300 K. The isentropic efficiency of each compressor and turbine is 80% and the regenerator effectiveness is also 80%. Determine (a) the thermal efficiency. Use the IG model for air. (b) What-if Scenario: What would the thermal efficiency of the cycle be if the turbine and compressor efficiency increased to 90%? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 44.1%, (b) 53.8%
8-1-31 [ericsson-115kPa] Consider an ideal Ericsson cycle with air as working fluid executed in a steady-flow system. Air is at 30 o C and 115 kPa at the beginning of the isothermal compression process during which 155 kJ/kg of heat is rejected. Heat transfer to air occurs at 1250 K. Determine (a) the maximum pressure in the cycle, (b) the net work output per unit mass of air and (c) the thermal efficiency of the cycle. Use the PG model. [Edit Problem] [TEST Solution]
Answers: (a) 683.6 kPa, (b) 484.4 kJ/kg, (c) 75.76%
Anim. 8-1-31(click)
8-1-32 [ericsson-1200K] Air enters the turbine of an Ericsson cycle at 1000 kPa, 1200 K, with a mass flow rate of 1 kg/s. The temperature and pressure at the inlet to the compressor are 250 K and 100 kPa respectively. Determine (a) the thermal efficiency of the cycle, (b) the net work output per unit mass of air. Use the PG model. [Edit Problem] [TEST Solution]
Answers: (a) 79%, (b) 628 kJ/kg
Fig. 8-1-32
8-1-33 [ericsson-1500kPa] Hydrogen enters the turbine of an Ericsson cycle at 1500 kPa, 900 K, with a mass flow rate of 1 kg/s. The temperature and pressure at the inlet to the compressor are 320 K and 150 kPa respectively. Determine (a) the thermal efficiency of the cycle, (b) the net work output per unit mass of air. Use the PG model. (b) What-if Scenario: How would the answers change if the IG model were used? [Edit Problem] [TEST Solution]
Answers: (a) 64%, (b) 5496 kJ/kg, (c) No change
Section-2: Momentum Equation and Jet Engines
8-2-1 [pipe-100kgs] Liquid water flows through a pipe at a mass flow rate of 100 kg/s. If the cross-sectional area of the pipe is 0.01 m 2 , determine (a) the flow rate of momentum through the pipe. [Edit Problem]
Answers: (a) 1 kN
8-2-2 [hose-400gpm] A firefighter is trying to hold a fire hose steady while spraying water. If the jet of water ( density 997 kg/m 3 ) is coming from the 6.5-cm diameter fire hose at 400 GPM (0.025 m 3 /s), what is the force required by the firefighter to hold the hose steady? [Edit Problem]
Answers: 0.19 kN
Anim. 8-2-2(click)
8-2-3 [rocket-700mps] A rocket motor is fired on a test stand. Hot exhaust gases leave the exit with a velocity of 700 m/s at a mass flow rate of 10 kg/s. The exit area is 0.01 m 2 and the exit pressure is 50 kPa. For an ambient pressure of 100 kPa, determine the rocket motor thrust that is transmitted to the stand. Assume steady state and one-dimensional flow. [Edit Problem] [Manual Solution]
Answers: 6.5 kN
Anim. 8-2-3(click)
8-2-4 [nozzle-450mps] A jet engine is traveling through the air with a velocity of 150 m/s. the exhaust gases leave the nozzle with an exit velocity of 450 m/s with respect to the nozzle. Pressure at the inlet and exit are 30 kPa and 100 kPa respectively, and the ambient pressure is 30 kPa. If the mass flow rate is 10 kg/s and the exit area is 0.2 m 2 , determine the jet thrust. [Edit Problem]
Answers: 17 kN
Anim. 8-2-4(click)
8-2-5 [turbo-6000m] A turbojet aircraft is flying with a velocity of 300 m/s at an altitude of 6000 m, the ambient conditions are 45 kPa and -15 o C. The compressor pressure ratio is 14 and the turbine inlet temperature is 1500 K. Assuming ideal operation of all components and constant specific heats, determine (a) the pressure at the turbine exit, (b) the velocity of the exhaust gases and (c) the propulsive efficiency. (d) What-if Scenario: What would the velocity of the exhaust gases be if the aircraft velocity were 200 m/s? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 447 kPa, (b) 1059 m/s, (c) 26.5%, (d) 1033 m/s
Anim. 8-2-5(click)
8-2-6 [compressor-90kPa] A jet engine is being tested on a test stand. The inlet area to the compressor is 0.2 m 2 and air enters the compressor at 90 kPa, 100 m/s. The pressure of the atmosphere is 100 kPa. The exit area of the engine is 0.1 m 2 , and the products of combustion leave the exit at a pressure of 130 kPa and a temperature of 1000 K. The air fuel ratio is 45 kg air/kg fuel, and the fuel enters with a low velocity. The mass flow rate of air entering the engine is 10 kg/s. Determine (a) the inlet temperature, (b) the exit velocity of combustion products and (c) the thrust on the engine. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 627.20 K, (b) 225.61 m/s, (c) 5.31 kN
8-2-7 [tmax-1200C] Consider an ideal jet propulsion cycle in which air enters the compressor at 100 kPa and 20 o C. The pressure leaving the compressor is 1100 kPa, and the maximum temperature in the cycle is 1200 o C. Air expands in the turbine at which the turbine work is equal to the compressor work. On leaving the turbine, air expands in a nozzle to 100 kPa. The process is reversible and adiabatic. Determine (a) the velocity of the air leaving the nozzle. Use the PG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 942 m/s
8-2-8 [tmax-1000C] Consider an ideal jet propulsion cycle in which air enters the compressor at 100 kPa and 25 o C. The pressure leaving the compressor is 1 MPa, and the maximum temperature in the cycle is 1000 o C. Air expands in the turbine at which the turbine work is just equal to the compressor work. On leaving the turbine, air expands in a nozzle to 100 kPa. The process is reversible and adiabatic. Determine (a) the velocity of the air leaving the nozzle. Use the PG model. (b) What-if Scenario: What would the exit velocity be if the maximum temperature achieved in the cycle were 800 o C? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 821.5 m/s, (b) 693.8 m/s
8-2-9 [turbo-9150m] A turbojet aircraft is flying with a velocity of 350 m/s at an altitude of 9150 m, the ambient conditions are 30 kPa and -30 o C. The pressure ratio across the compressor is 10, and the temperature at the turbine inlet is 1200 K. Air enters the compressor at a rate of 30 kg/s, and the jet fuel has a heating value of 42000 kJ/kg. Using the PG model, determine (a) the velocity of the exhaust gases, (b) the propulsive power developed and (c) the rate of fuel consumption. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 918.1 m/s, (b) 5982.9 kW, (c) 0.43 kg/s
Anim. 8-2-9(click)
8-2-10 [air-50kgs] A turbojet aircraft is flying with a velocity of 250 m/s at an altitude where the ambient conditions are 20 kPa and -25 o C. The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1000 o C . Air enters the compressor at a rate of 50 kg/s. Determine (a) the temperature and pressure of the gases at the turbine exit, (b) the velocity of the gases at the nozzle exit and (c) the propulsive efficiency of the cycle. Use the PG model. (d) What-if Scenario: What would the exit velocity be if the aircraft velocity were 300 m/s? [Edit Problem] [TEST Solution]
Answers: (a) 147.4 kPa, 984 K, (b) 927 m/s, (c) 24 %, (d)
8-2-11 [air-20kgs] Consider an aircraft powered by a turbojet engine that has a pressure ratio of 10. The aircraft is stationary on the ground,held in position by its brakes. The ambient air is 25 o C and 100 kPa and enters the engine at a rate of 20 kg/s. The jet fuel has a heating value of 42700 kJ/kg, and it is burned completely at a rate of 0.35 kg/s. Neglecting the effect of the diffuser and disregarding the slight change in the mass at the engine exit as well as the inefficiencies of the engine components, determine (a) the force that must be applied on the brakes to hold the plane stationary. Use IG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 16.584 kN
8-2-12 [chamber-25000kJs] Air at 10 o C enters a turbojet engine at a rate of 15 kg/s and at a velocity of 320 m/s (relative to the engine). Air is heated in the combustion chamber at a rate of 25000 kJ/s and it leaves the engine at 420 o C. Determine (a) the thrust produced by this turbojet engine. Use the IG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 19320 N
8-2-13 [compressor-80pct] Repeat problem 8-2-9 using a compressor efficiency of 80% and turbine efficiency of 85%. Determine (a) the velocity of the exhaust gases, (b) the propulsive power developed and (c) the rate of fuel consumption. [Edit Problem] [TEST Solution]
Answers: (a) 788.1 m/s, (b) 4600 kW, (c) 0.38 kg/s
Anim. 8-2-13(click)
8-2-14 [diffuser-80kPa] Air enters the diffuser of a turbojet engine with a mass flow rate of 65 kg/s at 80 kPa, -40 o C and a velocity of 245 m/s. The pressure ratio for the compressor is 10, and its isentropic efficiency is 87%. Air enters the turbine at 1000 o C with the same pressure as the exit of the compressor. Air exits the nozzle at 80 kPa. The turbine has an isentropic efficiency of 90%.Determine (a) the rate of heat addition, (b) the compressor power input and (c) the velocity of the air leaving the nozzle. Use the IG model. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 53.2 MW, (b) 18.33 MW. (c) 915.4 m/s
8-2-15 [turbo-10000m] Air at 30 kPa, 250 K and 250 m/s enters a turbojet engine in flight at an altitude of 10,000 m. The pressure ratio across the compressor is 12. The turbine inlet temperature is 1400 K, and the pressure at the nozzle exit is 30 kPa. The diffuser and nozzle processes are isentropic, the compressor and turbine have isentropic efficiencies of 85% and 80%, respectively, and there is no pressure drop for flow through the combustor.Using the IG model, determine (a) the velocity of the exhaust gases. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 958 m/s
8-2-16 [nozzle-1300K] Consider the addition of an afterburner to the turbojet engine in 8-2-15 that raises the temperature at the inlet of the nozzle to 1300 K.Using the IG model, determine (a) the velocity at the nozzle exit. (b) What-if Scenario: What would the exit velocity be if the temperature at the inlet of the nozzle were 1200 K ? [Edit Problem] [TEST Solution]
Answers: (a) 1039.5 m/s, (b) 997 m/s
Anim. 8-2-16(click)
8-2-17 [ram-50kPa] Air enters the diffuser of a ramjet engine at 50 kPa, 230 K, with a velocity of 480 m/s, and is decelerated to a velocity of zero. After combustion, the gases reach a temperature of 1000 K before being discharged through the nozzle at 50 kPa. Using IG model, determine (a) the pressure at the diffuser exit and (b) the velocity at the nozzle exit. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 206 kPa, (b) 825 m/s
8-2-18 [ram-200K] Air enters the diffuser of a ramjet engine at 25 kPa, 200 K, with a velocity of 3000 km/h, and is decelerated to a negligible velocity. On the basis of an air standard analysis, the heat addition is 870 kJ/kg of air passing through the engine. Air exits the nozzle at 25 kPa.Using the IG model, determine (a) the pressure at the diffuser exit, and (b) the velocity at the nozzle exit. (c) What-if Scenario: What would the exit velocity be if the heat addition were 1200 kJ/kg? [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (a) 842 kPa, (b) 1328 m/s, (c) 1467.6 m/s
Anim. 8-2-18(click)
Section-3: Exergy Analysis of Gas Turbines
8-3-1 [ter-1500C] In an air standard Brayton cycle, air enters the compressor at 0.1 MPa, 20 o C (atmospheric conditions) and a mass flow rate of 10 kg/s. The pressure leaving the compressor is 1 MPa, and the maximum temperature in the cycle is 1225 o C. If the heat addition can be assumed to take place from a reservoir at 1500 o C, (a) perform an exergy inventory and draw an exergy flow diagram for the cycle. Determine (b) the thermal efficiency and (c) the exergetic efficiency. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (b) 48.2% (c) 57.7%
Anim. 8-3-1(click)
8-3-2 [compressor-80pct] Repeat problem 8-3-1 assuming a compressor efficiency of 80% and a turbine efficiency of 80%. [Edit Problem] [Manual Solution]
Answers: (b) 81.8%, (c) 23.2%
Anim. 8-3-2(click)
8-3-3 [ter-1800K] Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 290 K and a mass flow rate of 6 kg/s. The compressor pressure ratio is 10. The turbine inlet temperature is 1500 K. A regenerator with an effectiveness of 70% is incorporated in the cycle. If the heat addition can be assumed to take place from a reservoir at 1800 K, (a) perform an exergy inventory and draw an exergy flow diagram for the cycle. Determine (b) the thermal efficiency and (c) the exergetic efficiency. (d) Calculate the rate of exergy destruction in the regenerator. [Edit Problem] [Manual Solution] [TEST Solution]
Answers: (b) 57.50%, (c) 68.89%, (d) 40.03 kW
Anim. 8-3-3(click)
| Version No: 24; Last Updated: 2010-10-31 11:02:17 | Copyright 1998-2010: Subrata Bhattacharjee |