Water flows over the bump in the bottom of the rectangular channel shown in the figure below with a flowrate per unit width of q = 4 m²/s. The channel bottom contour is given by zB = 0.2e¯** where zg and x are in meters. The water depth far upstream of the bump is y1 0.4 m. Calculate (a) the water depth, y, and (b) the surface elevation, z, for x = 0.5 m. Assume one-dimensional flow. (a) y = i (b) z= i m 3 V₁ 31 y(x) z(x) -x -0.2

Determine the depth in a trapezoidal channel with side slopes of 1 to 1.5, a bottom width of 8 1. m and a channel slope 0.0009. The discharge is 56 m3/s and n = 0.017. Make the sketch of the figure showing the different parameters; top width B, bottom width b, flow area A, flow depth y and side slope s. Sketch: y m Please follow the format in answering 1. Given 2. Required 3. Solution (with explanations)

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Water is flowing in a trapezoidal channel at a rate of Q = 20 m³/s. The critical depth y for such a channel must satisfy the equation: 1 -3 B = 0 where g = 9.81 m/s?, Ac =the cross-sectional area (m?), and B = Q? the width of the channel at the surface (m). For this case, the width and the cross-sectional area can be related to depth y by B = 3 + y and A. = 3y +: Solve for the critical depth using bisection method using the initial guesses x = 0.5 and xu = 2.5.