A pitot intake on a supersonic aircraft flies at Mach $M_0 = 1.8$. A normal shock stands at the inlet lip. For $\gamma = 1.4$, what is the total pressure recovery ratio $p_{01}/p_{00}$ across the normal shock? (Round off to three decimal places).

Answer Key:

0.813

### Solution: Normal shock total pressure ratio for $\gamma = 1.4$: $\frac{p_{01}}{p_{00}} = \left(\frac{\gamma + 1}{2\gamma M_0^2 - (\gamma - 1)}\right)^{\frac{1}{\gamma - 1}} \left(\frac{(\gamma + 1)M_0^2}{2 + (\gamma - 1)M_0^2}\right)^{\frac{\gamma}{\gamma - 1}}$. For $M_0 = 1.8$, standard normal shock table yields $p_{01}/p_{00} = 0.8127 \approx 0.813$. Correct: 0.813 (range 0.805 to 0.820).

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