QUESTION $4\mathrm{.}1$

A rectangular channel connects two reservoirs and has a slope of $0\mathrm{.}001.$ The channel has a width of $10$ m and a Manning $\text{'}n\text{'}$ of $0\mathrm{.}03.$ If the upstream reservoir surface is $3\mathrm{.}5$ m above the invert of the outlet,

$($a$)$ determine the discharge in the channel.

$($b$)$ Given the same channel which is hydraulically mild and that it is $240$ m long, show that for a $Q=75\frac{m^3}{s},$ the downstream lake level is $2\mathrm{.}8$ m above the brink. Sketch the flow profile for this ase.