QUESTION $2$

A flood attenuation basin is to be constructed at the outlet of a catchment to protect a development

downstream. The catchment has a plan shape that may be approximated as a quarter circle with a

radius of $360m.$ Water will flow radially over the catchment towards the outlet at the circle centre at a

velocity of $0\mathrm{.}30\frac{m}{s}.$

The basin will be square in plan with $30m$ sides, a horizontal bottom and vertical side walls. Water will

flow out of the basin through a pipe with its entrance at the bottom of the basin and over a weir with its

crest $2\mathrm{.}0m$ above the bottom of the basin. The discharge through the pipe is given by

$Q=0\mathrm{.}87h^{\frac{1}{2}}$

where $h$ is the height of the water surface above the bottom of the basin. The discharge over the weir is

given by

$Q=3\mathrm{.}6H^{\frac{3}{2}}$

where $H$ is the height of the water surface above the weir crest.

The excess rain hyetograph for the selected design storm is given in the table below.

Determine

a$.$ the maximum discharge leaving the basin, and

b$.$ the minimum height required for the side walls of the basin.

$($The basin will be empty at the beginning of the storm. For constructing the Storage Indication Curve

use water levels from $0$ to $3\mathrm{.}0m$ in steps of $0\mathrm{.}50m.)$