Horizontal Tank Volume with Dished Heads (Dipstick)

The straight shell is the circular-segment prism (the flat-end result), and the two curved heads together form an ellipsoid, so their partial fill is the spherical cap scaled by the head depth: V_heads = (b/R)(pi h^2/3)(3R - h), with b = R/2 for a 2:1 semi-elliptical (ASME dished) head and b = R for a hemispherical head. An 8 ft, 20 ft-shell tank half full (4 ft) holds 4,261 gal with 2:1 heads (67 ft^3 of it in the heads) or 4,763 gal with hemispherical heads, against 3,760 gal for flat ends - the heads add 13% to 27%. Enter the straight-shell (seam-to-seam) length; the heads are added on. Flat-ended tanks are gauged separately. A close estimate; the tank's strapping chart governs custody transfer.

shell = [R^2 acos((R-h)/R) - (R-h) sqrt(2Rh-h^2)] L; heads = (b/R)(pi h^2/3)(3R-h), b = R/2 (2:1 elliptical) or R (hemispherical); full = pi R^2 L + (b/R)(4/3) pi R^3.

Horizontal-tank partial gauging - the straight shell is the circular-segment prism and the two dished heads form an ellipsoid whose partial fill is an affine-scaled spherical cap; standard tank-gauging geometry as in Machinery's Handbook (Industrial Press) and API 2551 manual-tank-strapping practice, by name; public domain.

Public-domain solid geometry; the diameter, shell length, depth, and head type are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: diameter_ft, shell_length_ft, fill_depth_ft, head_type, volume_gal, percent_full, heads_volume_ft3

• Shell partial volume circular-segment prism, area x shell length (the flat-end tank-volume result)plane/solid geometry
• Head partial volume (b/R)(pi h^2/3)(3R-h), b = R/2 elliptical or R hemisphericalaffine-scaled spherical cap
• Scope 2:1 elliptical or hemispherical heads; flat heads are the tank-volume tile, torispherical is a close approximationscope of this tile