The specific impulse of the jet engine.
Answer to Problem 170RP
The specific impulse of the jet engine is
Explanation of Solution
Draw the
Consider that the aircraft is stationary, and the velocity of air moving towards the aircraft is
Diffuser :
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:
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:
Write the temperature relation for the compressor and turbine.
Here, the specific heat at constant pressure is
, temperature at state 4 is
Nozzle:
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.
Write the expression to calculate the specific impulse of the jet engine.
Here, the thrust force produced by engine is
Conclusion.
From Table A-1E, “Molar mass, gas constant, and critical-point properties”, obtain the
value of gas constant
From Table A-2Ea, “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 10psia for
Substitute 9 for
Substitute 609.8 R for
Substitute
Substitute
The rate of change in the energy of the system
Substitute
Here, velocity at stat 5 is
Since,
Substitute
Substitute
Thus, the specific impulse of the jet engine is
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