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Critical to Stagnation Pressure ratio $$\left(\frac{P^*}{P_0}\right)$$ for an expansion process is
$$\frac{P^*}{P_0} = \left[\frac{2}{\gamma + 1}\right]^{\frac{2 \gamma}{(\gamma - 1)}}$$
$$\frac{P^*}{P_0} = \left[\frac{2}{\gamma + 1}\right]^{\frac{(\gamma + 1)}{(\gamma - 1)}}$$
$$\frac{P^*}{P_0} = \left[\frac{2}{\gamma + 1}\right]^{\frac{\gamma}{(\gamma + 1)}}$$
$$\frac{P^*}{P_0} = \left[\frac{2}{\gamma + 1}\right]^{\frac{\gamma}{(\gamma - 1)}}$$
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