A turbojet aircraft is flying with a velocity of 280 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and −32°C. The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1100 K. Air enters the compressor at a rate of 50 kg/s, and the jet fuel has a heating value of 42,700 kJ/kg. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the velocity of the exhaust gases, (b) the propulsive power developed, and (c) the rate of fuel consumption.
a)
The velocity of the exhaust gases.
Answer to Problem 136P
The velocity of the exhaust gases is
Explanation of Solution
Draw the
Consider, the pressure is
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 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.
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.
Turbine (For process 4-5)
Write the temperature relation for the compressor and turbine to calculate the temperature at state 5
Nozzle (For process 5-6)
Write the temperature and pressure relation for the isentropic process 4-6.
Write the expression for the energy balance equation for the nozzle.
Conclusion:
From Table A-2a, “Ideal-gas specific heats of various common gases”, obtain the following values of air at room temperature.
The rate of change in the energy of the system
Substitute
Here, the specific heat at constant pressure of air is
Substitute 0 for
Substitute 32 kPa for
Substitute 12 for
Substitute 280.0 K for
Substitute 1,100 K for
For process 5-6 (Nozzle)
Substitute 1100 K for
The rate of change in the energy of the system
Substitute
Substitute 810.5 K for
Thus, the velocity of the exhaust gases is
b)
The propulsive power produced by the turbojet engine.
Answer to Problem 136P
The propulsive power produced by the turbojet engine is
Explanation of Solution
Nozzle (For process 5-6)
Write the expression to calculate the propulsive power produced by the turbojet engine
Here, the velocity of the aircraft is
engine is
Conclusion:
Substitute
Thus, the propulsive power produced by the turbojet engine is
c)
The rate of fuel consumption.
Answer to Problem 136P
The rate of fuel consumption is
Explanation of Solution
Write the expression to calculate the heating value of the fuel for the turbojet engine
Write the expression to calculate the mass flow rate of fuel for the turbojet engine
Here, the calorific value of the fuel is HV.
Conclusion.
Substitute
Substitute
Thus, the rate of fuel consumption is
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Chapter 9 Solutions
THERMODYNAMICS
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