Horizontal vessel: volume at a level
Liquid volume in a partly filled horizontal cylindrical vessel (storage tank, drain vessel, separator, settling tank): the cylinder segment plus flat, 2:1 ellipsoidal or hemispherical heads.
A = R² · arccos((R − h) / R) − (R − h) · √(2 · R · h − h²)V = A · L + (a / R) · π · h² · (3 · R − h) / 3a = 0; D/4 (2:1); D/2 (hemispherical)The heads are treated as parts of an ellipsoid of depth a (D/4 for 2:1, D/2 for hemispherical). Torispherical heads can be approximated as ellipsoidal; conical heads are not covered. For custody measurement use the vessel's calibration table.
Source: Geometry of a circular segment and an ellipsoid cap; ellipsoidal heads — GOST 6533-78
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Tangent to tangent; include the straight flanges of the heads in L.
From the bottom of the shell.
Unit converter for this formulaLength · Density and °API · Liquid volume · Mass · Fraction and percent
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- V/V_tot — Fill by volume–
- V_tot — Total vessel volume–
- M — Liquid mass–
More in Tanks and vessels
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.