= Solution
Orient the flow so $q>0$, and let subscripts 1 and 2 denote upstream and downstream. The mechanical <energy flux> is $\rho q B$, where $B=u^2/2+gh$. Inserting the relation for $q^2$ in <3/a/i> gives the <hydraulic jump head loss>,
$$
B_1-B_2=\frac{q^2}{2}\left(\frac1{h_1^2}-\frac1{h_2^2}\right)+g(h_1-h_2)=\frac{g(h_2-h_1)^3}{4h_1h_2}.
$$
An admissible jump dissipates mechanical <energy>, so $\rho q(B_1-B_2)>0$. The denominator is positive, hence
$$
\boxed{h_2>h_1}.
$$
The zero depth-change case is continuous flow. A depth-decreasing discontinuity would require an energy input at the jump; it is not the dissipative <hydraulic jump> selected by this model.
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