For a convergent nozzle discharging air ($\gamma = 1.4$), the critical pressure ratio $\left(\frac{p^*}{p_0}\right)$ at which choking occurs at the throat is approximately:

(A) 0.528

(B) 0.685

(C) 0.450

(D) 0.712

Answer Key:

A

### Solution: Critical pressure ratio: $\frac{p^*}{p_0} = \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma}{\gamma - 1}} = \left(\frac{2}{2.4}\right)^{3.5} = (0.8333)^{3.5} \approx 0.5283$. Correct: A.

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