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`V = f( "L" , "D" , "R" , "a" )`

Enter a value for all fields

The **Torispherical Head Tank Volume** calculator computes the volume of a cylindrical tank with torispherical heads (dish end) based on the length (L) and diameter (D) of the tank and the crown radius (R) and knuckle radius (a) of the torispherical heads.

**INSTRUCTIONS:** Choose units and enter the following:

- (
**L**) Length of Tank - (
**D**) Diameter of Tank - (
**R**) Interior Crown Radius of Torispherical Head - (
**a**) Interior Knuckle Radius of Torispherical Head

**Volume of a Cylindrical Tank with Torispherical Heads (V):** The volume is returned in cubic meters. However, the volume can be automatically converted to other volume units (e.g. liters, cubic feet, gallons, barrels) via the pull-down menu.

The relationship between the diameter of a torispherical head and the height of the head is:

`h = R - sqrt((R-a)^2 - (D/2 -a)^2)`

where:

- h = torispherical head height
- R = crown radius
- a = knuckle radius

The formula for the volume of an Torispherical Head is as follows:

`V = π/3[2⋅h⋅R²-(2a² + c² + 2aR)(R-h)+3a²c sin‾¹( (R-h)/(R-a))]`

where:

- V is the volume of the Torispherical Head
- R is the crown radius
- h is the head height.
- a is the knuckle radius

The value of c is computed from R, h and a as follows:

`c = sqrt( (R-a)² - (R-h)² )`

The Diameter (D) is simply:

D = 2(c+a)

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