A reservoir is filled with water of density ρ. The depth of the water is ℎ. A gate is used to block the water on the right side as shown in the figure. The gate is hinged at the free surface level (z...

A reservoir is filled with water of density ρ. The depth of the water is ℎ. A gate is used to block the water on the right side as shown in the figure. The gate is hinged at the free surface level (z = 0), and a cable is attached to the gate ℎ/2 above the hinge. Compute how much pulling force F is needed to keep the gate closed. The atmospheric pressure is a constant p=p0 in case needed. The width (horizontal length) of the gate is W.