what should be the dimensions and side slopes of the channel to obtain the maximum discharge?

Water flows down a trapezoidal open channel that has a bottom width B of 4.0m and a water surface width BS of 17.2m when the depth of flow on the channel centreline is 3.3m. (a) Without using any charts or tables, calculate the value of the wetted perimeter, the hydraulic radius and the hydraulic mean depth. (b) If the optimum hydraulic section for a trapezoidal channel is half of a hexagon, prove that the top width of the channel is 2.309D where D is the centreline depth. (c) If D = 3.3m, what should be the dimensions and side slopes of the channel to obtain the maximum discharge?

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