Question

A tank with a square base of area 1.0 m² is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm². The tank is filled with water in one compartment, and an acid(of relative density 1.7) in the other, both to a height of 4.0 m, compute the force necessary to keep the door close.

Answer 1

Area of base of the tank = 1.0 m²

Area of compartment, A = 0.5 m²

Height of water or acid in each compartment, h = 4 m

Density of water, ρ_w = 1000 kg m^-3

Density of acid, ρ_a = 1.7 x 1000 kg m^-3

= 1700 kg m^-3

Net pressure on the door,

p = Pressure of acid - Pressure of water

= ρ_agh -ρ_wgh = (p_a - p_w)gh

= (1700 - 1000) x 9.8 x 4

= 700 x 9.8 x 4

= 2.744 x 10⁴ Pa

Now, area of the door,

a = 20 cm² = 20 x 10^-4 m²

Force on the door, F = p x a = 2.744 x 10⁴ x 20 x 10⁴ = 54.88 N