อัปเดต 2026-09-07

Vessel Volume & Liquid Level

Tank strapping / dip-chart — Jones (1974) closed-form; ASME VIII UG-32 heads

Contained liquid volume (or its inverse: the level for a target volume) in horizontal/vertical cylindrical vessels fitted with flat, hemispherical, 2:1-ellipsoidal, or ASME torispherical (F&D) heads.

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Splits the vessel into the cylindrical shell (a circular-segment cross-section swept along the length) plus two head partial-volumes — closed-form spherical-cap scaling for hemispherical/ellipsoidal heads, adaptive-Simpson integration of the segment-area profile for torispherical heads (split at the knuckle/crown junction) — then inverts V(h) for a target volume via monotone bisection. The h=R half-full symmetry gives a zero-tolerance regression anchor for any head type.

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Circular Segment (Wetted) Area

A (R, h) = R^{2} cos^{- 1} (\frac{R - h}{R}) - (R - h) 2 R h - h^{2}

Disc of radius R wetted to height h; the shell cross-section for a horizontal cylinder (Jones 1974).

Horizontal Shell Partial Volume

V_{s h e l l} = A (R, h) \cdot L

Circular-segment area swept along the cylindrical (tan-to-tan) length L.

Hemispherical Head Partial Volume (per head)

V_{h e a d} = \frac{1}{2} \cdot \frac{π h ^{2}}{3} (3 R - h)

Spherical-cap formula; two hemispherical heads together form one sphere of radius R (ASME BPVC VIII-1 UG-32(f)).

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