Math Question

Dan, U.S. Air Force, retired wrote:
Matt Whiting wrote:

W P Dixon wrote:

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will
see if yall can come up with it. Yes I did check on the web, but did
not see the formula I need.
I want to figure the volume of a gas tank that will not be round
or square, It will have five sides and then the two ends of the tank.
With one end being larger than the other. I would give exact
measurements , but being as I don't know what they will be yet I
can't:} I need to find the right volume in order to get the right
measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on how irregular the tank shape is, you may have to solve
this using numerical integration. However, if the tank shape is the
same in at least one axis (say z or vertical), then figure the area of
the shape in the x-y plane and then simply multiply times the height,
z, and equate that to the volume you desire. Then solve for z.


Matt


That would work if it had the same cross sectional area along Z. He says
otherwise. This leaves to 3 solutions: 1) build it, fill it and measure
the volume coming out, 2) calculus which would be quickest and easiest
or 3) draw a diagram, cut it into solids you can calculate, then add up
the volume of the solids.

If the small end isn't very much smaller than the big end go ahead and
do it Matt's way and add a fudge factor.

I'd find an ME student at a local university and have them create a
solid model of the tank using SolidWorks, ProE or similar. You can then
get an accurate volume with the press of a key. And you can play "what
if" with the design until the cows come home.


Matt