Question

The greatest and the least depth of a circular plate of 4 m diameter from the free surface of water are 3m and 1 m respectively as shown. What will be the depth (in m) of it’s centre of pressure?

(a) 1.125

(b) 1.25

(c) 2.125

(d) 2.25

I had been asked this question in a national level competition.

I'd like to ask this question from Hydrostatic Force on Plane Area in section Hydrostatic Forces on Surfaces of Fluid Mechanics

Answer 1

The correct option is (c) 2.125

Explanation: The depth of the centroid y and the centre of pressure yCP are related by:

where I= the moment of inertia and A = area and θ = the angle of inclination of the lamina to the horizontal. Now,

y = 1 + 3 – 1 / 2 = 2, I = ^π ⁄ 64 * 4^2 = 4π,  A = ^π ⁄ 4 * 4^2 = 4π, sin θ = ^1 ⁄ 2 Thus, yCP = 2.125m.