# word problem for hydrostatic force

• Jun 23rd 2009, 06:10 PM
eniuqvw
word problem for hydrostatic force
a large tank designed with ends in the shape of the region between the curves y=(x^2)/3 and y = 14 measured in feet. Tank is filled to a depth of 12 feet with gas. The pressure of gas is 42.0 lb/(ft^3). I'm supposed to find the pressure exerted on one end of the tank with this information. I'm having trouble interpreting this and finding the solution.
• Jun 23rd 2009, 09:56 PM
CaptainBlack
Quote:

Originally Posted by eniuqvw
The pressure of gas is 42.0 lb/(ft^3).

That should be the density of the gasoline not pressure.

Also don't use the term "gas" this is an international forum and a substantial proportion of readers think "gas" refers to a gas.

(Also$\displaystyle ^2$ the use of US customary units is deprecated, but you can't do anything about that, its your teacher/educational system that is at fault on that (and NASA apparently)).

The force on a horizontal area element $\displaystyle ds$ is the weight of the fluid $\displaystyle w$ above it ($\displaystyle w=g\, \rho\, h\, ds$ where $\displaystyle h$ is the height of fluid above the area element), and as pressure is isotropic this is also the force on a vertical area element $\displaystyle ds$. So to get the pressure on an end face you integrate this over the face and divide by the area of the face.

Note: the formula for the weight I gave is for a consistent set of units and $\displaystyle g$ is the acceleration due to gravity, you will need to sort out the units of force/mass for US customary units for yourself. In SI units this weight will be in Newtons

CB
• Jun 23rd 2009, 11:34 PM
eniuqvw
I'm not sure i agree with the dismissive attitude but thanks anyway, i figured it out a while ago.
• Jun 24th 2009, 03:51 AM
mr fantastic
Quote:

Originally Posted by eniuqvw
I'm not sure i agree with the dismissive attitude but thanks anyway, i figured it out a while ago.