The net force acting on the gate element of width dy at a depth y from the surface of the fluid, is dy = (p0+ρgy−p0) × 1 dy = ρgydy Torque about the hinge is dτ = pgydy × (
1
2
−y) Net torque experienced by the gate is
τnet = ∫ dτ + F ×
1
2
=
1
∫
0
ρg ydy (
1
2
−y) + F ×
1
2
= 0 ⇒ F =
ρg
6
i.e., The force F required to hold the gate stationary is