Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am looking for an equation to calculate the volume of liquid in an underground tank based on a depth reading.

The tank is an ellipsoid shape with the following dimensions:

X-Axis Radius:    30.425 cm
Y-Axis Radius:    30.425 cm
Z-Axis Radius:    60.95 cm 

I am trying to find an equation that would provide the volume of liquid in liters at a specific depth: For example:

When the tank is filled up with liquid to:
30cm (1/2 way) 
the volume of liquid would be around:  
120 Liters.

And when the tank if filled up to the top:
60cm
the volume would be around:  
240 Liters.

Thank you for your assistance!

share|improve this question

1 Answer 1

up vote 3 down vote accepted

Let the semi-axes (the 'radii') in each direction be $r_x$, $r_y$, and $r_z$, and let the depth of the liquid be $d$. Squeeze (or stretch) the ellipsoid into a sphere of unit radius, so that all of these are $1$; the depth of the liquid is then $d' = d/r_z$, and its volume is $\pi d'^2(3-d')/3$, as you know from your previous question. Now stretch (or squeeze) the sphere back into its original shape, thus expanding the volume of the liquid by a factor $r_xr_yr_z$.

share|improve this answer
    
Thank you Tony! That makes it quite clear for me. So the equation in its entirety would be: π * (d/rz)^2*(3−(d/rz))/3 * rxryrz. –  Synergistca Jan 25 '11 at 23:44
    
@Synergistca: Yes. –  TonyK Jan 26 '11 at 14:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.