a)
The velocity of the exhaust gases
a)
Answer to Problem 137P
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 expression to calculate 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 expression to calculate the pressure relation using the pressure ratio for the process 2-3.
Here, the pressure ratio is
Write the expression to calculate the temperature and pressure relation for the process 2-3s.
Write the expression for the efficiency of the compressor in the turbojet engine
Here, the specific heat of air at constant pressure is
Turbine (For process 4-5)
Write the expression for the temperature relation for the compressor and turbine.
Write the expression for the efficiency of the turbine in the turbojet engine
Write the expression to calculate the temperature and pressure relation for the process 4-5.
Nozzle (For process 5-6)
Write the expression to calculate the temperature and pressure relation for the isentropic process 4-5.
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
Equation (XI).
Substitute 32 kPa for
Substitute 12 for
Substitute 280.0 K for
Substitute 0.80 for
Substitute 1100 K for
Substitute 0.85 for
Substitute 674.2 K for
Substitute 738.1 K for
The rate of change in the energy of the system
Substitute
Substitute 738.1 K for
Hence, the velocity of the exhaust gases is
b)
The propulsive power produced by the turbojet engine
b)
Answer to Problem 137P
The propulsive power produced by the turbojet engine is
Explanation of Solution
Write the expression to calculate the propulsive power produced by the turbojet engine
Here, the mass flow rate of air through the engine is
Conclusion:
Substitute
Hence, the propulsive power produced by the turbojet engine is
c)
The rate of fuel consumption.
c)
Answer to Problem 137P
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
Hence, the rate of fuel consumption is
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Chapter 9 Solutions
CONNECT FOR THERMODYNAMICS: AN ENGINEERI
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