Air flows supersonically at Mach $M_1 = 2.0$ through a normal shock wave. If the upstream static pressure is $p_1 = 50\text{ kPa}$ and ratio of specific heats $\gamma = 1.4$, what is the downstream static pressure $p_2$ (in kPa)?

Answer Key:

225

### Solution: Normal shock pressure ratio: $\frac{p_2}{p_1} = 1 + \frac{2\gamma}{\gamma + 1}(M_1^2 - 1) = 1 + \frac{2(1.4)}{2.4}(4 - 1) = 1 + \frac{2.8}{2.4}(3) = 1 + 3.5 = 4.5$. Downstream pressure $p_2 = 4.5 \times 50 = 225\text{ kPa}$. Correct: 225.

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