= Solution
Use the steady inviscid, hydrostatic, slowly varying channel approximation, without a <hydraulic jump>. Conservation of volume flux per unit width gives $Q=u(x)h(x)=u_1h_1$. The free-surface <Bernoulli equation> is
$$
D(x)+h(x)+\frac{Q^2}{2gh(x)^2}=h_1+\frac{u_1^2}{2g}.
$$
Dividing by $h_1$ yields
$$
\boxed{\frac D{h_1}=1-\frac h{h_1}-\frac F2\left(\frac{h_1^2}{h^2}-1\right),\qquad F=\frac{u_1^2}{gh_1}.}
$$
The parameter $F$ here is the squared upstream <Froude number>. For nonzero discharge, regarding $D$ as a function of $h$, its <derivative> is $dD/dh=-1+Q^2/(gh^3)$. It has its unique maximum at $h_c=(Q^2/g)^{1/3}=h_1F^{1/3}$, where the local <Froude number> is one. Substitution gives $D^*=h_1(1-3F^{1/3}/2+F/2)$. This maximum is the <hydraulic control over a smooth hump>.
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