Question

A gate of length 5 m is hinged at A as shown to support a water column of height 2.5 m. What should be the minimum mass per unit width of the gate to keep it closed?

(a) 3608

(b) 4811

(c) 7217

(d) 9622

I had been asked this question in a job interview.

This key question is from Hydrostatic Force on Plane Area topic in portion Hydrostatic Forces on Surfaces of Fluid Mechanics

Answer 1

Correct choice is (d) 9622

Easy explanation: To keep the gate closed, moment due to weight of the gate should be balanced by the moment due to the hydrostatic force.

where m = mass of the plate, θ = angle of inclination to the horizontal, Fhyd = hydrostatic force on

the plate, x = distance of the point of action of Fhyd from the hinge point = ^2⁄3 * 5 = ^10⁄3

Fhyd = γyA, where γ = specific weight of the liquid = 9.81 * 10^3 y = depth of the centre of pressure from the free surface = 2.5/2 = 1.25 and A = 5 * 1. Substituting all the values in the equation, we get m = 9622.5g.