Horizontal Cylinderical Tanks

Tanks are used for the storage fluids in many chemical process industries. For a horizontal cylinderical tank, the two ends (heads) of the vessels is usually both flat, dished, elliptical or hemispherical. It is commonly required to estimate the quantity of fluid in a tank when it is partly filled with fluid, and only fluid level is known. This partial volume is made up of the volume in the cylinderical shell plus the volumes in the two heads. The partial volumes can be estimated by the equations below:
Partial volume of horizontal cylinder:
    = {r²cos^-1[(r - h)/r] - (r - h)(2rh - h²)^0.5}L
Partial volume of dished heads:
    = 0.215483*h²(1.5d - h)
Partial volume of elliptical heads:
    = 0.5236*h²(1.5d - h)
Partial volume of hemispherical heads:
    = 1.0472*h²(1.5d - h)
where
     L = side length of the cylinder shell
     d = internal diameter of the cylinder
     r = radius of the cylinder = d/2
     h = height of liquid in the cylinder
All volume equations give fluid volumes in cubic units from tank dimensions in consistent linear units.