Question

A square lamina (each side equal to 2m) with a central hole of diameter 1m is submerged vertically in water such that the upper edge of the lamina is at a depth of 0.5 m from the free surface. What will be the total water pressure (in kN) on the lamina?

(a) 15.77

(b) 31.54

(c) 47.31

(d) 63.08

This question was addressed to me in examination.

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

Answer 1

Correct option is (c) 47.31

Explanation: Total liquid pressure on the lamina = F = γyA, where γ = specific weight of the liquid, y = depth of centroid of the lamina from the free surface, A= area of the centroid. Now, γ = 9:81 * 10^3 N / m^3; y = 0.5 + ^1 ⁄ 2 * 2m = 1.5 m, A = 2 * 2 – ^π ⁄ 4 * 1^2 m^2 = 3.215 m^2 Hence, F = 47.31 kN.