Water flows over a bump of height h h(x) on the bottom of

Chapter 10, Problem 10.32

(choose chapter or problem)

Water flows over a bump of height h = h(x) on the bottom of a wide rectangular channel as is indicated in Fig. P10.32. 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, = 0, or > 0) of dy/dx relative to the sign of dh/dx.