$4.$ A sluice gate is lowered into a rectangular channel. The velocity of flow upstream is $\backslash (2\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and the Specific Energy upstream is $2\mathrm{.}2$ m $.$

a$.$ Calculate the depth upstream $($ y $1)$

$[4]$

b$.$ Calculate the Specific Discharge $($discharge per unit width$)$

$[2]$

c$.$ Calculate the Critical Depth for this flow

$[2]$

d$.$ Is the flow upstream Sub$-$Critical? Or Super$-$Critical?

$[4]$

e$.$ If the gate opening $($ yg $)$ is set at $1\mathrm{.}4$ m $,$ will the water depths upstream be different from those downstream?

$[3]$