A rectangular gate hinged at the bottom separates a tank into two compartments, one containing water and the other containing oil, as shown in Figure $4-11.$ The depth of the water is $6\mathrm{.}5$ ft and the height of the gate is $6$ in$.$ The oil has a specific gravity of $0\mathrm{.}77.$ Initially the water and the oil are at the same depth, and the gate remains firmly closed, because the pressure due to the water is greater than that due to the oil. The oil depth is then increased, and the force on the right side of the gate becomes larger and more nearly counterbalances the force on the left. Find the height of the oil, h$\_\{2\}$ at which the gate will just open and allow oil to bubble into the water.