Question

A 6-m-hight, 4-m-wide rectangular gate is located at the end of an open freshwater tank. The gate is hinged at the top and held in place by a force F. The pressure is proportional to the depth of the water and the average pressure p_avg exerted on the gate by the water is: where deltap is the difference in pressure between the bottom of the gate (P_1) and the surface (p_0). The resulting force of the water on the gate is F_water = P_avg A where A is the area of the gate the water acts upon. The resulting force acts 2 m from the bottom of the gate because the pressure increases with depth. Determine the force required to hold the gate in place.

Answer 1

Using equiibrium of momentum @ the hinge,

F_water* (6-2) = F*(3)

Force required, F = F_water*(4/3) = 4/3*P_avg * A=(4/3)*delta(P) /2* A=2/3* (P₁-P₀)*A