Question

A large aquarium of height 6 m is filled with fresh water to a depth of D = 1.50 m. One wall of the aquarium consists of thick plastic with horizontal length w = 8.40 m. By how much does the total force on that wall increase if the aquarium is next filled to a depth of D = 4.30 m? (Note: use g = 9.81 m/s2 and rho = 998 kg/m3.)

Answer 1

Answer

given,

height of aquarium = 6 m

Depth of fresh water = D = 1.50 m

horizontal length of the aquarium(w) = 8.40 m

total force increased when liquid is filled to depth = 4.30 m

g = 9.81 m/s²

ρ = 998 Kg/m³

force in the aquarium.

dF = PdA

$F = \int PdA$

$F = \int \rho\ g\ y\ (wdy)$

$F = \rho\ g\ w \int ydy$

$F = \rho\ g\ w\dfrac{y^2}{2}$

$F = \dfrac{\rho\ g\ w\ y^2}{2}$

At D = 1.5 m

$F = \dfrac{980\times 9.8\times 8.4\times 1.5^2}{2}$

F = 9.08 x 10⁴ N

At D = 4.30 m

$F = \dfrac{980\times 9.8\times 8.4\times 4.3^2}{2}$

F = 7.46 x 10⁵ N

Total force on the wall increased by

ΔF  = 74.6 x 10⁴ - 9.08 x 10⁴

ΔF  = 65.52 x 10⁴ N