A trapezoidal concrete$-$lined channel has a constant bed slope of $0003,$ a bed width of $5\mathrm{.}9$ m and side slopes $1$:$4$ and carries a discharge of $75\mathrm{.}0$ m$3/$s$.$ The channel terminates in a free outfall as shown in Figure $1$ below. Take n $=0025$ and $=1\mathrm{.}0$ Prepare a short report to include the following:

a$)$ Calculate the normal depth of flow for this channel.

b$)$ Calculate the critical depth for this flow.

c$)$ Identify the type of flow occurring in this channel and hence classify the bed slope.

d$)$ Identify the control points you would use to compute the water surface profile upstream of the free outfall. $($refer to slides $36-38$ of Lecture $4)$

e$)$ What type of water surface profiles do you expect and explain why? f$)$ By using a $$y $=0\mathrm{.}02$ m in the direct step method, compute and plot the water surface profile upstream of the free outfall. You may construct an excel spreadsheet to perform these calculations.

g$)$ State all assumptions made.

h$)$ Sample hand calculations must be submitted for at least the first $2$ steps in your values table.