Engineering calculators · Storage

Tank volume and dip table calculator

Find the volume of liquid in a tank from its level, or the level for a given volume, and print a dip table. It covers vertical tanks with flat or cone bottoms, horizontal tanks with flat or hemispherical ends, and rectangular tanks, which between them cover most chemical dosing, buffer, sludge and storage tanks.

Inputs

Use internal dimensions. Depth is measured from the lowest point inside the tank. For a vertical tank, the straight-side height excludes any cone. For a horizontal tank, the length is the straight shell between the ends. The default density is water at 20 °C [NIST].

Results

Volume at this depth14.1 m³14,137 L, 14.1 t
Full volume28.3 m³internal height 4.00 m
Fill level50%ullage 14.1 m³
Depth for target volume–enter a volume

Dip table

Depth, mVolume, m³Volume, L% of full
0000%
0.4002.832,82710%
0.8005.655,65520%
1.208.488,48230%
1.6011.311,31040%
2.0014.114,13750%
2.4017.016,96560%
2.8019.819,79270%
3.2022.622,61980%
3.6025.425,44790%
4.0028.328,274100%

How the calculation works

  • Vertical cylinder: V = πR²y.
  • Cone bottom: up to the cone height the liquid is a conical frustum, V = πy(r₀² + r₀r + r²)/3, where r₀ is the outlet radius and r is the radius at the liquid surface [frus]. Above the cone, add πR² for each metre of straight side.
  • Horizontal cylinder: V = L × segment area, where the segment area is R² arccos(1 − y/R) − (R − y)√(y(2R − y)) [seg].
  • Hemispherical ends: the two ends together make a sphere, so add the spherical cap πy²(3R − y)/3 [cap].
  • Rectangular: V = L × W × y.
  • Depth for a volume is found numerically, and mass = volume × density.

What this cannot tell you. It assumes a perfectly regular shape. It does not include torispherical or elliptical dished heads, sloping floors, internal pipework, baffles or mixers, or a tank that is out of level. For custody transfer or stock accounting, calibrate the tank by strapping or by metered filling.

Sources

  1. Wikipedia: Circular segment (area from radius and height)
  2. Wikipedia: Spherical cap (volume πh²(3r − h)/3)
  3. Wikipedia: Frustum (volume of a conical frustum)
  4. NIST Chemistry WebBook: Isobaric properties of water at 0.101325 MPa (density and viscosity, 0–100 °C)

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