Question

A trapezoidal channel having a bottom slope of 0.001 is carrying a flow of 75 m³/s. The channel bottom is 50 m wide, n = 0.025, and the channel side slopes are 1 vertical to 1.5 horizontal. If a control structure is built at the downstream end that raises the water depth at the downstream end to 12 m, determine the amount by which the channel banks must be raised along its length. Assume the channel had uniform flow prior to the construction of the control structure.

Answer 1

Answer:normal depth=0.749m

Explanation:Discharge:==1ℎ2/31/2Hence,=1ℎ2/3(1+2ℎ/1+2√5ℎ/)2/31/2ℎ(1+2ℎ/)√=ℎ5/3(1+2ℎ/)5/3(1+2√5ℎ/)2ℎ=(√)3/5(1+2√5ℎ/)2/51+2ℎ/Here, with lengths in metres,ℎ=0.8316(1+1.491ℎ)2/51+2ℎ/3Iteration (from, e.g., ℎ=0.8316)givesℎ=0.7487 m