Dished Tank / Vessel Head Volume
The liquid volume of one dished tank head (the bulge past the tangent line), plus any straight-flange skirt: 2:1 semi-elliptical = pi D^3/24; hemispherical = pi D^3/12; ASME flanged-and-dished (torispherical) ~ 0.0847 D^3; straight flange = pi/4 D^2 x length; gallons = in^3/231. A 48 in ID 2:1 elliptical head holds 62.7 gal (14,477 in^3); a hemispherical head of the same diameter holds 125.3 gal, an F&D head 40.5 gal. Two heads make a tank's end allowance beyond the straight-shell volume; the F&D figure is a standard-geometry approximation, the head maker's stamped crown and knuckle radii govern the exact volume. Complements the flat-end tank-volume gauging tile.
Formula and source
2:1 semi-elliptical head V = pi D^3 / 24; hemispherical V = pi D^3 / 12; ASME flanged-and-dished (torispherical) V ~ 0.0847 D^3; straight flange V = pi/4 D^2 x length; gallons = in^3 / 231.
Dished-head volume geometry, first-principles; the inside diameter, head type, and straight-flange length come from the head. The ASME F&D figure is a standard-geometry approximation.
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