Question $2$: A broad$-$crested weir allows water from a reservoir to access an overflow spillway $($Fig$.$ Q$2).$ It can be demonstrated that the change from subcritical to supercritical flow happens close to the weir crest when the spillway's flow is supercritical.

$($a$)$ If the weir's width is $46$ meters, make necessary assumptions and derive the relationship between the spillway flow rate $(Q)$ and the water level $H.$

$($b$)$ A peak flow of $97\mathrm{.}2\frac{m^3}{s}$ was recorded at the gauging station downstream of the spillway. Determine the reservoir's equivalent water level.