Question

A cylindrical flask of radius (a) containing a static fluid of density (ρ) is filled to height (H). The atmospheric pressure on the free surface of the fluid is (P_ATM) and the gravitational acceleration is (g). Develop an equation for the average force exerted by the fluid on the side walls of the flask.

Answer 1

Let elementary area of flask = dA

Thickness of the element at a distance of y = dy

Pressure applied to wall = P

From the pascal's law, Pressure applies to the every point of the flask.

Pressure on the element taken

P = Patm + gy

Force exerted on walls of elementary area = dF

dF = PdA

F = dF = PdA

F = (gy + Patm) (2a dy)

F = gy (2a dy) + Patm (2a dy)

F = [2a g ydy] + [Patm x 2a dy]

F = [ 2ag (y²/2)₀^H ] + [Patm x 2a (y)₀^H]

F = 2ag (H²/2) + Patm x 2a H

F = 2aH [g (H/2) + Patm]