A rectangular retention basin is designed to attenuate a target flood wave as shown in the figure. The inflow hydrograph of the flood wave is of a triangular shape of peak discharge at $0\mathrm{.}21\frac{m^3}{s}$ and duration of $50$min. The corresponding design outflow hydrograph is also of a triangular shape with peak discharge at $0\mathrm{.}12\frac{m^3}{s}.$

$($a$)$ Calculate the required storage of the retention basin.

$(5$ marks$)$

$($b$)$ The retention basin has a single$-$stage primary spillway with a rectangular weir of length $L.$ The weir crest is at a level $2\mathrm{.}2m$ above the bottom of the basin. During the time of peak outflow discharge $($at $30$min from the start of the target flood wave$),$ the design water depth in the basin is $2\mathrm{.}5m.$ Determine the required length of the weir $($correct to the nearest $0\mathrm{.}01m)$ so that it will provide the required peak outflow when the water depth is $2\mathrm{.}5m?$ Assume a discharge coefficient of $0\mathrm{.}7$ for the weir.

$(7$ marks$)$

$($c$)$ For the outflow from the basin to follow the outflow hydrograph as shown in the figure, when should be the water depth in the basin at the start of the flood wave?

$(3$ marks$)$