A pure jet engine propels an aircraft at 240 m/s through air at 45 kPa and −13°C. The inlet diameter of this engine is 1.6 m, the compressor pressure ratio is 13, and the temperature at the turbine inlet is 557°C. Determine the velocity at the exit of this engine’s nozzle and the thrust produced. Assume ideal operation for all components and constant specific heats at room temperature.
The velocity at the exit of this engine’s nozzle and the thrust produced.
Answer to Problem 132P
The velocity at the exit of this engine’s nozzle is
The thrust produced by the 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
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 volume at state 1
Here, gas constant is
Write the expression to calculate the mass flow rate of propeller
Here, propeller diameter is
Write the expression to calculate the thrust force generated by the propeller
Here, the thrust force produced by engine is
Conclusion.
From Table A-2a, “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
Substitute
Substitute
The rate of change in the energy of the system
Substitute
Here, velocity at stat 5 is
Since,
Substitute
Thus, the velocity at the exit of this engine’s nozzle is
Substitute
Substitute
Substitute
Thus, the thrust produced by the engine is
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