Water flows over a bump of height (h=h(x)) on the bottom of a wide rectangular channel as

Question:

Water flows over a bump of height $h=h(x)$ on the bottom of a wide rectangular channel as is indicated in Fig. P10.25. If energy losses are negligible, show that the slope of the water surface is given by $d y / d x=-(d h / d x) /\left[1-\left(V^{2} / g y\right)\right]$, where $V=V(x)$ and $y=y(x)$ are the local velocity and depth of flow. Comment on the sign (i.e., $0$ ) of $d y / d x$ relative to the sign of $d h / d x$.

Figure P10.25