a)
The pressure at the turbine exit.
a)
Answer to Problem 133P
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 temperature and 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 temperature and pressure relation for the process 2-3.
Here, temperate 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 temperature and pressure relation for the process 4-5.
Conclusion:
From Table A-2E, “Ideal-gas specific heats of various common gases”, obtain the following values for air at room temperature.
The rate of change in the energy of the system
Substitute
Here, inlet velocity is
Substitute 0 for
Substitute
Substitute 13 for
Substitute 537.4 R for
Substitute
Substitute
Thus, the pressure at the turbine exit is
b)
The exit velocity of the exhaust gases.
b)
Answer to Problem 133P
The exit velocity of the exhaust gases is
Explanation of Solution
Nozzle (For process 5-6)
Write the temperature and pressure relation for the isentropic process 4-6.
Here, pressure at state 6 is
Write the energy balance equation for the nozzle.
Conclusion:
Substitute
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.
c)
Answer to Problem 133P
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, temperature 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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Chapter 9 Solutions
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