Question two

a$.$ A trapezoidal channel having Manning's $n=0\mathrm{.}012$ is to be constructed to carry stormwater. The slope of the ground surface is $1$ in $600$ and the design discharge is $2\mathrm{.}5\frac{m^3}{s}.$ Calculate the proportions of the trapezoidal channel that will minimise excavation and result in the optimum hydraulic section. $(10$ marks$)$

b$.$ If the conditions in $($a$)$ above were not changed but a rectangular channel was used instead of a trapezoidal channel, what would be the dimensions of the optimum hydraulic section?