How to calculate part volume in an round horizontal tank with flat end, dish end and having elliptical ends.?

Question

To make simple if we have water filled in a horizontal tank at periodical heights what would be water quntity ie when the tank is filled 1/4th then 1/2 then 3/4th and full upto brim for all options of flat end, Dish end and elliptical end.

Answer 1

The general method is to use the fact that the volume at any level h is the integral of the surface area at h times h.. For example, if the horizontal cross-section of the tank at any level x is a rectangle (flat end) or a rectangle plus a part of a circle (dish end) or an ellipse (elliptical ends), write a formula for the cross-section area as a function of x, call this A(x). The volume at level h is then

V(h) = integral(0 to h) of A(x)*dx

The difficult part is finding A(x) which can get very messy. In the case of the flat ends, if the tank has length L and radius R, the area function A(x) = 2*sqrt[2*R*x - x^2] so the integral becomes

V(h) = integral(0 to h) 2*sqrt[2*R*x - x^2]*dx

The A(x) for the other end shapes is A(x) as above, plus the added area of the ends.

(Edited)
EDIT AGAIN: I left out the length in the area formula. The correct result is

V(h) = integral(0 to h) 2*sqrt[2*R*x - x^2]*L*dx

The same result is obtained by multiplying the area of a circular segment of altitude h by the length L. However, that method does not work for the dish and elliptical ends; the integration process demonstrates the approach to use.

Answer 2

The diameter (in feet) divided by 2 = N
Then N * N* 3.142 * the height you want (in feet) = FT3
FT3 * 7.48 = Gallons
Gallons * 42 = Barrels (Oil U.S.)
Ex. How many gallons in a 5 FT Diameter Tank that is 2 FT High.
Answer = 19.6 FT3 or 146.9 Gallons

Answer 3

http://unicon.netian.com/tank_vol_e.html

This link gives you partial tank volume calculations for almost all configurations.

This is an online calculator for elliptical dished ends.
http://www.abe.msstate.edu/~fto/tools/vol/ellipsetank1.html

Also, check Perrys