Consider a subsonic compressible flow in cartesian coordinates where the velocity potential is given by
If the freestream properties are given by
The Mach number of the subsonic compressible flow.
The temperature of the subsonic compressible flow.
The pressure of the subsonic compressible flow.
Answer to Problem 11.1P
The Mach number for the fluid at the given point is
The pressure for the fluid at the given point is
The temperature for the fluid at the given point is
Explanation of Solution
Given:
The freestream velocity of the compressible flow is
The pressure of the compressible flow is
The temperature of the compressible flow is
Formula used:
The velocity component in the x-direction is given as,
The velocity component in the y-direction is given as,
The expression for the Mach number is given as,
Here,
The velocity of the flow is given as,
The expression for the temperature for the given point is given as,
The expression for the pressure is given as,
Calculation:
The “Properties of air” is given as,
The velocity component of the fluid in x-direction can be calculated as,
The velocity component of the fluid in the y-direction can be calculated as,
The resultant velocity of the flow can be calculated as,
The Mach number of the supersonic flow can be calculated as,
For
The pressure at starts can be calculated as,
The required temperature can be calculated by the energy equation as,
The required Mach number can be calculated as,
The required pressure for the flow can be calculated as,
Conclusion:
Therefore, the Mach number for the fluid at the given point is
Therefore, the pressure for the fluid at the given point is
Therefore, the temperature for the fluid at the given point is
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