The pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock and Compare for helium undergoing a normal shock under the same conditions.
Answer to Problem 90P
The Mach number value of air after the normal shock through the nozzle is
The actual temperature of air after the normal shock through the nozzle
is
The actual pressure of air after the normal shock through the nozzle is
The stagnation pressure of air after the normal shock though the nozzle
is
The velocity of air after the normal shock through the nozzle is
Thus, the Mach number of helium gas after the normal shock through the nozzle
is
Thus, the actual temperature of helium after the normal shock through the nozzle is
Thus, the actual pressure of helium after the normal shock through the nozzle
is
Thus, the stagnation pressure of helium after the normal shock though the nozzle
is
Thus, the velocity of helium after the normal shock through the nozzle is
Comparison between the obtained results of air and helium is shown in below Table:
Parameters/ Conditions | Air | Helium |
Mach number value | ||
Actual temperature of air | ||
Actual pressure of air | ||
Stagnation pressure | ||
Velocity |
Explanation of Solution
Write the expression for the velocity of sound after the normal shock.
Here, velocity of sound after the shock is
Write the expression for the velocity of airafter the normal shock.
Write the expression for the Mach number for helium after the normal shock.
Here, Mach number of helium before the normal shock is
before the normal shock is
Write the expression for the actual pressure of helium gas after the normal shock.
Here, actual pressure of helium after the shock is
Write the expression for the actual temperature of helium gas after the normal shock.
Here, actual temperature of helium after the shock is
Write the expression for the actual pressure of helium gas after the normal shock.
Here, stagnation pressure of helium after the shock is
Write the expression for the velocity of sound after the normal shock.
Here, velocity of sound after the shock is
Write the expression for the velocity of helium after the normal shock.
Conclusion:
Refer to Table A-33, “One-dimensional normal-shock functions for an ideal gas with k 5 1.4”, obtain the expressions of temperature ratio, pressure ratio, stagnation pressure ratio, and Mach number after the shock for a Mach number of 2.6 before the shock.
Thus, the Mach number value of air after the normal shock through the nozzle is
Here, actual pressure after the shock is
Substitute
Thus, the actual temperature of air after the normal shock through the nozzle
is
Substitute
Thus, the actual pressure of air after the normal shock through the nozzle is
The actual pressure before the normal shock is the same as the stagnation pressure before the normal shock
Substitute
Thus, the stagnation pressure of air after the normal shock though the nozzle
is
Refer to thermodynamics properties table and interpret the value of k, and R for a temperature of
Substitute 1.4 for k,
Substitute 0.5039for
Thus, the velocity of air after the normal shock through the nozzle is
Substitute 2.6for
Thus, the Mach number of helium gas after the normal shock through the nozzle
is
Substitute 1.667 for k, 2.6for
Substitute 1.667 for k, 2.6for
Substitute 1.667 for k, 2.6for
Substitute
Thus, the actual temperature of helium after the normal shock through the nozzle is
Substitute
Thus, the actual pressure of helium after the normal shock through the nozzle
is
Since,
Substitute
Thus, the stagnation pressure of air after the normal shock though the nozzle
is
Refer Table A–1, “Molar mass, gas constant, and critical2point properties”, obtain
the value of k, and R for a temperature of
Substitute 1.667 for k,
Substitute 0.5455 for
Thus, the velocity of air after the normal shock through the nozzle is
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Chapter 17 Solutions
CENGEL'S 9TH EDITION OF THERMODYNAMICS:
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