A $3\mathrm{.}8-$m$-$wide, $10-$m$-$high rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown below. The gate is hinged at its bottom and held closed by a horizontal force, FH$,$ located at the center of the gate. The maximum value for FH is $4,453$ kN$.$ Determine the maximum water depth, h $($in meters$),$ above the center of the gate that can exist without the gate opening.