c) A rectangular concrete channel has a broad crested weir at its downstream end similar to that in Figure 3 below, the channel is 10 m wide, has a slope of 1m/km and a Manning n= 0.012. For a discharge of 150 m3/s.

= [a Q/gb], where Q is the (a) Show that the critical depth for rectangular channels is expressed by y. discharge, b is the channel width, and a is the energy coefficient. (b) A half trapezoid flood drainage channel (Fig. 3b) has a flow of 100 m³/s. If the flow depth upstream of the 0.2 m step-rise is 4 m, what is the depth at an immediately downstream section of the 0.2 m step- rise? Assume there are no losses in the transition. Also compute the flow depth at the a very far downstream end if the flood drainage channel ends in a free overfall. (c) For a symmetrical compound channel section (Fig. 3c), compute the n., α, and S, based on the assumption that the depth of flow in the section is 5 m; the flood plains and the main channel have the same bottom slope of 0.001; and roughness coefficient for the main channel and the flood floodplains are respectively 0.021 and 0.039.