A turbojet is flying with a velocity of 900 ft/s at an altitude of 20,000 ft, where the ambient conditions are 7 psia and 10°F. The pressure ratio across the compressor is 13, and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the pressure at the turbine exit, (b) the velocity of the exhaust gases, and (c) the propulsive efficiency.
9–134E Repeat Prob. 9–133E accounting for the variation of specific heats with temperature.
a)
The pressure at the turbine exit.
Answer to Problem 130P
The pressure at the turbine exit is
Explanation of Solution
Draw the
Consider that the aircraft is stationary, and the velocity of air moving towards the aircraft is
Diffuser (For process 1-2):
Write the expression for the energy balance equation for the diffuser.
Here, the rate of energy entering the system is
Write the pressure and relative pressure relation for the process 1-2.
Here, the specific heat ratio of air is k, pressure at state 1 is
Compressor (For process 2-3)
Write the pressure relation using the pressure ratio for the process 2-3.
Here, the pressure ratio is
Write the pressure and relative pressure relation for the process 2-3.
Here, pressure at state 3 is
Turbine (For process 4-5)
Write the temperature relation for the compressor and turbine.
Here, the specific heat at constant pressure is
Write the pressure and relative pressure relation for the process 4-5.
Here, pressure at state 5 is
Conclusion:
From Table A-17E, “Ideal-gas properties of air”, obtain the following properties at the temperature of
The rate of change in the energy of the system
Substitute
Here, inlet velocity is
From Table A-17E, “Ideal-gas properties of air”, obtain the following properties at the temperature of
Substitute 0 for
Substitute
Substitute 13 for
Substitute
From the Table A-17, “Ideal-gas properties of air” obtain the values of enthalpy on
Substitute
in Equation (V).
From the Table A-17, “Ideal-gas properties of air” obtain the values of relative pressure
Substitute
Thus, the pressure at the turbine exit is
b)
The exit velocity of the exhaust gases.
Answer to Problem 130P
The exit velocity of the exhaust gases is
Explanation of Solution
Nozzle (For process 5-6)
Write the pressure and relative pressure relation for the process 5-6.
Here, pressure at state 6 is
Write the energy balance equation for the nozzle.
Conclusion:
Substitute
From the Table A-17, “Ideal-gas properties of air” obtain the values of enthalpy on
The rate of change in the energy of the system
Substitute
Here, velocity at stat 5 is
Since,
Substitute
Thus, the exit velocity of the exhaust gases is
c)
The propulsive efficiency of the turbojet engine.
Answer to Problem 130P
The propulsive efficiency of the turbojet engine is
Explanation of Solution
Write the expression to calculate the propulsive work done per unit mass by the turbojet engine
Here, the velocity of the aircraft is
Write the expression to calculate the heating value of the fuel per unit mass for the turbojet engine
Here, enthalpy at state 4 is
Write the expression to calculate the propulsive efficiency of the turbojet engine
Conclusion.
Substitute
Substitute
Substitute
Thus, the propulsive efficiency of the turbojet engine is
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- A turbojet is flying with a velocity of 900 ft/s at an altitude of 20,000 ft, where the ambient conditions are 7 psia and 10°F. The pressure ratio across the compressor is 13, and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine the propulsive efficiency.arrow_forwardFor a specified compression ratio, is a diesel or gasoline engine more efficient?arrow_forwardAir is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of 100 percent.arrow_forward
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