Program and solve the differential equation of “frictionless flow over a bump,” for entrance conditions V0 = 1 m/s and y0 = 1 m. Let the bump have the convenient shape h = 0.5hmax [1 − cos (2π x/L)], which simulates Fig. P10.62. Let L = 3 m, and generate a numerical solution for y(x) in the bump region 0 < x < L. If you have time for only one case, use hmax = 15 cm (Prob. 10.63), for which the maximum Froude number is 0.425. If more time is available, it is instructive to examine a complete family of surface profiles for hmax ≈ 1 cm up to 35 cm.