The gate ABC, hinged at $C,$ is used as a flood protection for a river bank. The river depth to the horizontal wall, $h$ is $2\mathrm{.}5m.$ Part $BC$ of

the gate is designed as a quarter ellipse of radius $(a=2\mathrm{.}5m$;$b=0\mathrm{.}5m).$ The length $AB$ of the gate is at angle $=35$ with the

positive horizontal. The gate is $3\mathrm{.}4m$ wide $($into the page$),$ and ignore its weight. As the river level increases, the gate will get closer

to the bank. For a river depth of $H=5\mathrm{.}5m,$ find the total hydrostatic force due to pressure acting on the gate.