Question $3(20$ points$)$

In the City of Montreal, the water reservoir is located on top of Mont$-$Royal. A $5-$wide, $5-$high rectangular gate is installed to regulate the water level of the reservoir and prevent overflow. The gate is at the end of a rectangular passage as shown in the figure below. The gate is hinged at its top and held closed by a hydraulic system that results in a horizontal force, $F_H,$ located at the center of the gate. The maximum value for $F_H$ is $6500kN.$

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

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