Liquid Volume in Conical Tank Bottom

What is this formula?

Liquid Volume in Conical Tank Bottom calculates the liquid volume contained inside a partially filled conical tank bottom.

The formula is derived from the geometric similarity of cones. As the liquid level rises inside the cone, the liquid forms a smaller cone that is geometrically similar to the full conical bottom.

This equation is commonly used when the liquid level remains entirely inside the conical section.

When to use it

Use this formula when:

- h ≤ Hb

- the liquid level is completely inside the conical bottom

- the cylindrical section above the cone is still empty

Example

A storage tank has:

D = 12.0 m

Hb = 0.30 m

h = 0.15 m

Formula:

V = πD²h³/(12Hb²)

Substitution:

V = π×12²×0.15³/(12×0.30²)

Result:

V = 14.14 m³

The conical bottom contains approximately 14.14 m³ of liquid.

Applications

- Petroleum storage tanks

- Tank calibration tables

- Custody transfer calculations

- Water draw-off systems

- Inventory reconciliation

- Tank farm operations

Note

This formula is valid only while the liquid level remains inside the conical bottom.

Once the liquid height exceeds Hb, the conical bottom becomes completely full and additional volume accumulates in the cylindrical shell above the cone.

For that situation, a separate formula should be used:

Vertical Tank Liquid Volume Above Conical Bottom

which combines the full conical bottom volume with the cylindrical liquid volume above it.