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 × (21−y) Net torque experienced by the gate is
τnet = ∫ dτ + F × 21 = 0∫1 ρg ydy (21−y) + F × 21 = 0 ⇒ F = 6ρg i.e., The force F required to hold the gate stationary is 6pg
