# Math Help - word problem for hydrostatic force

1. ## 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.

2. 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 $^2$ 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 $ds$ is the weight of the fluid $w$ above it ( $w=g\, \rho\, h\, ds$ where $h$ is the height of fluid above the area element), and as pressure is isotropic this is also the force on a vertical area element $ds$. 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 $g$ 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

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

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