Question

A cuboidal tank is half filled with water. By what percent will the hydrostatic force on one of the vertical sides of the tank increase if it is completely filled?

Answer 1

By 300 %

Step-by-step explanation:

Let's start defining the cuboidal tank dimensions.

Their three dimensions are the same because its cuboidal ⇒

Tank volume =
`(h).(h).(h)=h^(3)`

Let's also define :

ρ = water density

g = gravity

The water hydrostatic force per unit width on a vertical side is

F = ρ.g.[(water height)^2].(1/2)

When the tank is half filled with water the force is (in the following equations I replace ρ.g by R):

`F1=R.((h)/(2))^(2).(1)/(2)\\F1=R.(h^(2))/(8)`

When the tank is completely filled the force is (remember that ρ.g = R):

`F2=R.h^(2).(1)/(2) \\F2=R.(h^(2))/(2)`

The force increased percently by :

`(F2-F1)/(F1).100=\\`

`F2-F1=R.(h^(2))/(2)-R.(h^(2))/(8)=(3)/(8).R.h^(2)`

`(F2-F1)/(F1)=((3)/(8).R.h^(2))/((R.h^(2))/(8))=3`

`(F2-F1)/(F1).100=3.(100)=300`

The percent is 300 %