An aircraft flies with a Mach number Ma1 = 0.9 at an altitude of 7000 m where the pressure is 41.1 kPa and the temperature is 242.7 K. The diffuser at the engine inlet has an exit Mach number of Ma2 = 0.3. For a mass flow rate of 38 kg/s, determine the static pressure rise across the diffuser and the exit area.
The static pressure rise across the diffuser and the exit area.
Answer to Problem 128RP
The pressure rise across the diffuser in the aircraft is
The exit area of the diffuser is
Explanation of Solution
Write the formula for velocity of sound at the inlet conditions.
Here, speed of sound at the inlet condition is
Write formula for the velocity of air at inlet.
Here, velocity of air after the normal shock is
Write the formula stagnation temperature of air at the inlet.
Here, actual (static) temperature of air at the inlet is
Consider the flow is isentropic.
Write the formula for stagnation pressure of air at inlet (isentropic condition).
Here, the static pressure of air at inlet is
Consider the diffuser is adiabatic and the inlet and exit enthalpies are equal.
When the stagnation temperatures are equal, the stagnation pressure are also equal.
Here, the static pressure of air at inlet is
Write the formula for velocity of sound at the exit conditions.
Here, speed of sound at the exit condition is
Write formula for the velocity of air at exit.
Here, the exit Mach number is
Write the formula stagnation temperature of air at the exit.
Here, actual (static) temperature of air at the inlet is
Write the formula for static pressure of air at exit (isentropic condition).
Here, the static pressure of air at inlet is
Write the formula for static pressure difference of air.
Write the formula for mass flow rate of air at exit condition.
Here, the exit cross sectional area is
Rearrange the Equation (X) to obtain
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2, “Ideal-gas specific heats of various common gases”.
The specific heat at constant pressure
The specific heat ratio
Conclusion:
Substitute
Substitute
Substitute
Substitute
Here,
Substitute 0.3 for
Substitute 282 K for
Equation (VII).
Substitute 1.4 for k,
Equation (VIII).
Substitute
Thus, the pressure rise across the diffuser in the aircraft is
Substitute
Substitute
Thus, the exit area of the diffuser is
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Chapter 17 Solutions
Thermodynamics: An Engineering Approach
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