A square gate of size 1 ~m 1 ~m is hinged at its mid-point. A fluid of density fills the space to the left of the gate. The force F required to hold the gate stationary is

Step-by-step solution

The net force acting on the gate element of width dy at a depth y from the surface of the fluid, is aligned dy &= ( p ₀+ _ g y - p ₀ ) 1 dy &= gydy aligned Torque about the hinge is d = pgydy ( 1 2 - y ) Net torque experience. by the gate is aligned _ net &= d + F 1 2 &= ₀¹ g ydy ( 1 2 - y )+ F 1 2 =0 & F = g 6 aligned i.e., The force F required to hold the gate stationary is p g a