Question

A large aquarium of height 5 m is filled with fresh water to a depth of D = 2.00 m. One wall of the aquarium consists of thick plastic with horizontal length w = 8.20 m. By how much does the total force on that wall increase if the aquarium is next filled to a depth of D = 3.90 m? (Note: use g = 9.81 m/s² and ρ = 998 kg/m³.)

Answer 1

F = 1/2 * (p * w * g * h^2)

where, p is the density of fresh water

Now,

They want the Difference in force,

So,

Lets call the force at 2.0 to be F1 and the Force at 3.90 m to be F2. Then we will call h1 2.0 m and h 2.0 m

F1 = 1/2 * (p * w * g * h1^2)

F2 = 1/2 * (p * w * g * h2^2)

And we want the difference, lets call that delta F,

Delta F = F2 - F1

Delta F = [1/2 * (p * w * g * h2^2)] - [1/2 * (d * w * g * h1^2)]

Delta F = 0.5 * p * w * g (h2^2 - h1^2)

DeltaF = 0.5* 998kg/m^3*8.20m*9.81m/s^2*((3.9m)^2-(2.0m)^2)

Delta F = 449.97 kN

I hope help you.