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

Answer:

By 300 %

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):

$F1=R.(\frac{h}{2})^{2}.\frac{1}{2}\\F1=R.\frac{h^{2}}{8}$

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

$F2=R.h^{2}.\frac{1}{2} \\F2=R.\frac{h^{2}}{2}$

The force increased percently by :

$\frac{F2-F1}{F1}.100=$

$F2-F1=R.\frac{h^{2}}{2}-R.\frac{h^{2}}{8}=\frac{3}{8}.R.h^{2}$

$\frac{F2-F1}{F1}=\frac{\frac{3}{8}.R.h^{2}}{\frac{R.h^{2}}{8}}=3$

$\frac{F2-F1}{F1}.100=3.(100)=300$

The percent is 300 %