Volume of Spherical Cap Section

• Feb 23rd 2009, 01:22 AM
babryce
Volume of Spherical Cap Section
So,

In calculating the volume of a partially-filled horizontal cylindrical tank which has ends similar to spherical caps, how do you calculate the volume of a partially-filled spherical cap (from the side of a sphere?)??

The cylinder I have solved, and the volume of a full spherical cap has been easy to find but the partial volume of the cap ends is tough.

This has been so hard for me to find information on, so I hope someone here has an idea!

The dimensions of this particular problem are: Cylinder Length = 8.16m, Diameter = 3.7m, Cap "height" (although horizontal) = 0.53m. I hope this is enough detail...
• Mar 2nd 2009, 11:20 AM
mateoc15
I'm not sure I understand the shape itself. Can you give a "real world" example of this shape? Picture would be really helpful too!
• Mar 5th 2009, 08:11 AM
babryce
For example the rounded end of a part-filled horizontal cylindrical tank, in this case.
• Mar 5th 2009, 08:25 AM
mateoc15
Something like this... ?

So the entire normal cylinder is filled, but the half-sphere cap is only partially filled?

http://lh3.ggpht.com/_RKF_hJBtDbg/Sa...0/Untitled.png
• Mar 5th 2009, 08:31 AM
babryce
Just like that, only rotated in x or z axis by 90 degrees so that the cylinder is in a horizontal position. The end is not hemispherical, but is the cap of a sphere with approximately double the diameter.
• Mar 5th 2009, 08:52 AM
mateoc15
Quote:

Originally Posted by babryce
The end is not hemispherical

Yikes... This one is ugly! Do you know the radius of that arc shape? Is it even a radius or is maybe part of an elliptical shape (even uglier)? If so I may have a way to find it, but I won't explain until I know whether it's radial.
• Mar 5th 2009, 09:03 AM
galactus