Horizontal Tank Volume with Hemispherical Heads

\[V=\frac{\pi D^2L}{4}+\frac{\pi D^3}{6}\]

Variables

Vtotal internal tank volume (m³)

Dinternal tank diameter (m)

Linternal cylindrical shell length (m)

Description

What is this formula?

Horizontal Tank Volume with Hemispherical Heads calculates the total internal volume of a horizontal cylindrical tank fitted with two hemispherical heads.

Because two hemispherical heads together form a complete sphere, the total vessel volume equals the cylindrical shell volume plus the volume of a sphere having the same diameter as the tank.

This configuration provides the highest volume contribution among the common head geometries.

When to use it

Use this formula when the vessel has a cylindrical shell and two hemispherical heads.

It is frequently used in high-pressure vessels, LPG storage tanks, cryogenic vessels, and process equipment.

Example

A vessel has:

D = 3.0 m

L = 8.0 m

Formula:

V = πD²L/4 + πD³/6

Substitution:

V = π×3²×8/4 + π×3³/6

Result:

V = 70.69 m³

The total vessel volume is approximately 70.69 m³.

Applications

- LPG vessels

- Pressure vessels

- Cryogenic tanks

- Process equipment

- Industrial storage tanks

- Capacity calculations

Note

Two hemispherical heads together form one complete sphere. Consequently, the head volume contribution is significantly larger than that of 2:1 elliptical or torispherical heads having the same diameter.