Prandtl shock relation ($u_1{u}_2=c_{\mathrm{cr}}^2$)

For a stationary normal shock in a polytropic perfect gas, the upstream and downstream normal speeds obey $u_1{u}_2=c_{\mathrm{cr}}^2$, where $c_{\mathrm{cr}}$ is the sonic speed on their common Bernoulli streamline.