A square of size 1 m × 1 m is hinged at its midpoint. A fluid of density r fills the space to the left of the gate. The force F required to hold the gas stationary is

At a depth y from the surface of the fluid, the net force acting on the gate element of width dy is dF = (p0+ρgy – p0) × 1dy =ρgy dy. Torque of this force about the hinge is dτ=ρgydy×12−y. Net torque experienced by the gate is τnet=∫dτ+F×12⇒∫01ρgydy12−y+F×12=0⇒F=ρg6