Past exam of the mathematics course of the University of Cambridge / 2009 / ib / Paper 1 / 17D / ii / Solution

The upstream flow is supercritical flow, with $h_1<h_c$. Now $dD/dh>0$, so the depth increases over the rising hump and the velocity decreases, while the free surface rises. Since $D_{\max }<D^{\ast }$, the depth stays below $h_c$. On the descending bed it decreases back to $h_1$ downstream, remaining supercritical throughout.