$3\mathrm{.}7$ A rectangular gate $($Fig$.3\mathrm{.}25)$ of negligible thickness, hinged at its top edge and of width $\backslash ($ b $\backslash ),$ separates two tanks in which there is the same liquid of density $\backslash (\backslash$rho $\backslash ).$ It is required that the gate shall open when the level in the left$-$hand tank falls below a distance $\backslash ($ H $\backslash )$ from the hinge. The level in the righthand tank remains constant at a height $\backslash ($ y $\backslash )$ above the hinge. Derive an expression for the weight of the gate in terms of $\backslash ($ H$,$ Y$,$ y$,$ b $\backslash )$ and $\backslash ($ g $\backslash ).$ Assume that the weight of the gate acts at its centre of area.