A $6-$m$-$wide, $8-$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 in Fig. The gate is hinged at its bottom and held closed by a horizontal force, $F_H,$ located at the center of the gate. The maximum value for $F_H$ is $4000$ kN $.($Consider $Y_{H2O}=9\mathrm{.}80k\frac{N}{m^3})$

$($a$)$ Determine the maximum water depth, $h,$ above the center of the gate that can exist without the gate opening.

$($b$)$ Is the answer the same if the gate is hinged at the top? Explain your answer.

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n$.$ Maximum depth of gate $,$ is less than maximum depth d at bottom.