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Question 2.8: A perfect gas flows isentropically through a nozzle. If the ...

A perfect gas flows isentropically through a nozzle. If the ratio of the nozzle exit to the throat is 3.0, and the exit Mach number is also 3.0, find the specific heats ratio of the gas.

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Given, A_{e}/A_{th}= 3.0 and M_{e} = 3.0.

For isentropic flow, the area–Mach number relation is

\frac{A_{e}}{A_{th}}=\frac{1}{M_{e}}\left [ \frac{2}{\gamma +1}\left ( 1+\frac{\gamma -1}{2} {M_{e}}^{2} \right ) \right ]^{\frac{\gamma +1}{2(\gamma -1)}}

 

The only way to solve for 𝛾 from the above equation is by trial and error.

By trial and error it can be found that \gamma = 1.67

This gas is a monatomic gas like helium or argon.

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