Horizontal Tank Volume with 2:1 Elliptical Heads

What is this formula?

Horizontal Tank Volume with 2:1 Elliptical Heads calculates the total internal volume of a horizontal cylindrical tank with two standard 2:1 elliptical heads.

A 2:1 elliptical head has a depth equal to one quarter of the tank diameter, so the total tank volume can be written using only the internal diameter and cylindrical shell length.

This is one of the most practical storage tank and pressure vessel volume formulas because 2:1 elliptical heads are widely used in industrial vessels.

When to use it

Use this formula when the tank has a horizontal cylindrical shell and two identical 2:1 elliptical heads.

It is especially useful for pressure vessels, process tanks, petroleum vessels, chemical storage tanks, and ASME-style vessel capacity calculations.

Example

A horizontal pressure vessel has an internal diameter of 3.0 m and an internal cylindrical shell length of 8.0 m.

Data:

D = 3.0 m

L = 8.0 m

Formula:

V = πD²L / 4 + πD³ / 12

Substitution:

V = π × 3.0² × 8.0 / 4 + π × 3.0³ / 12

Result:

V = 63.62 m³

The total internal volume of the tank is approximately 63.62 m³.

Applications

- 2:1 elliptical head tank capacity

- Horizontal pressure vessel volume

- Petroleum storage vessels

- Chemical process tanks

- ASME vessel calculations

- Industrial storage tank design

Note

This formula assumes two identical 2:1 elliptical heads, where each head depth equals D/4. If the head depth is different, use the general horizontal tank volume with ellipsoidal heads formula instead. For partially filled tanks, liquid level calculations require additional segment-volume methods and are not represented by this full-capacity formula.