$($a$)$ A vertical gate $2\mathrm{.}5$ metres high and $1\mathrm{.}8m$ wide is located on the upstream side of a flood

control structure to control the flow of stormwater into a pipe by sliding up and down on a pair

of rails.

Calculate the force on the gate when it is fully closed and the water just reaches the top of the

gate.

$($b$)$ A rectangular water reservoir is $10m5m$ in plan and is $5m$ deep, with vertical sides.

$($i$)$ Calculate the volume of water in the tank when the centres of pressure of each side are $1\mathrm{.}1$

metres above the base.

$($ii$)$ What additional volume of water must be added to the reservoir to double the hydrostatic

force on one of its sides?

$(3$ marks$)$