Concept explainers
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.
The pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock and for helium undergoing a normal shock under the same conditions.
Answer to Problem 80P
The actual temperature of air after the normal shock is
The actual pressure of air after the normal shock is
The stagnation pressure of air after the normal shock is
The Mach number value of air after the normal shock is
The velocity of air after the normal shock is
The Mach number of helium gas after the normal shock is
The actual temperature of helium after the normal shock is
The actual pressure of helium after the normal shock is
The stagnation pressure of air after the normal shock is
The velocity of air after the normal shock is
Explanation of Solution
Refer Table A-32, “One-dimensional isentropic compressible-flow functions for an ideal
gas with
Here, actual temperature after the shock is
Write the expression to calculate the velocity of sound after the normal shock.
Here, velocity of sound after the shock is
Write the expression to calculate the velocity of air after the normal shock.
The value from the table is not considered for Mach number
Write the expression to calculate the Mach number for helium after the normal shock.
Here, Mach number of helium before the normal shock is
Write the expression to calculate the actual pressure of helium gas after the normal shock.
Here, actual pressure of helium after the shock is
Write the expression to calculate the actual temperature of helium gas after the normal shock.
Here, actual temperature of helium after the shock is
Write the expression to calculate the actual pressure of helium gas after the normal shock.
Here, stagnation pressure of helium after the shock is
Write the expression to calculate the velocity of sound after the normal shock for helium.
Here, velocity of sound after the shock for helium is
Write the expression to calculate the velocity of helium after the normal shock
Conclusion:
For air:
Refer Table A-2E, “Ideal-gas specific heats of various common gases”, obtain the following properties for air at room temperature.
Substitute
Thus, the actual temperature of air after the normal shock is
Substitute
Thus, the actual pressure of air after the normal shock is
The actual pressure before the normal shock
Substitute
Thus, the stagnation pressure of air after the normal shock is
From Table A-32, “One-dimensional isentropic compressible-flow functions for an ideal
gas with
Thus, the Mach number value of air after the normal shock is
Substitute 1.4 for k,
Substitute 0.513 for
Thus, the velocity of air after the normal shock is
For helium:
Refer Table A-E, “Ideal-gas specific heats of various common gases”, obtain the following properties for helium.
Substitute 2.5 for
Thus, the Mach number of helium gas after the normal shock is
Substitute 1.667 for k, 2.5 for
Substitute 1.667 for k, 2.5 for
Substitute 1.667 for k, 2.5 for
Substitute
Thus, the actual pressure of helium after the normal shock is
Substitute
Thus, the actual temperature of helium after the normal shock is
Since the flow through the nozzle is isentropic
Substitute
Thus, the stagnation pressure of air after the normal shock is
Substitute
Substitute
Thus, the velocity of air after the normal shock is
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