Problem $4($P$2\mathrm{.}59)$

In the figure below, the rectangular gate AB has length $L$ and width $b($into the paper$).$ It is hinged at Point

B $,$ and has negligible weight. The liquid level $h$ remains at the top of the gate for any angle $.$

What is the total pressure force from the liquid on the gate? What is its line of action?

Find an analytical expression for the force $F,$ perpendicular to AB $,$ required to keep the gate in

equilibrium.

$A=bL$

$I_{}=\frac{b{L}^3}{12}$

$I_{xy}=0$