Torispherical Head Tank Volume

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 Math / Science

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)

Torispheric-head or Dished End Calculators

• Capacity of a Dished End Tank: Computes the volume of a cylindrical tank with torispherical heads based on the length and diameter of the tank and the crown radius and knuckle radius of the torispherical heads.
• Torispherical Head Volume: Computes the volume and diameter of an torispherical head (dish-head) based on the crown radius, knuckle radius and the height.
• Torispherical Head Volume and Height: computes the volume of an torispherical head based on the crown radius, knuckle radius and the Diameter. It also computes the head height. 
• Volume of a Torispherical Head Cylindrical Tank: Computes the volume of a cylindrical tank with torispherical heads (dish end) based on the length and diameter of the tank and the crown radius and knuckle radius of the torispherical heads.
• Mass of the Contents of Torispherical Head Tank: Computes the weight / mass of the contents of tank with torispherical heads based on the volume and density of the contents.

Storage Tank Calculators:

• Storage Capacity of a Rectangular Tank
• Above Ground Storage Tank Capacity
• Storage Capacity of a Horizontal Cylindrical Tank
• Fuel in a 268 Gallon Tank
• Fuel in a 322 Gallon Tank
• Fuel in a 150 Gallon Circular Tank
• Fuel in a 270 Gallon Circular Tank
• Fuel in a 525 Gallon Circular Tank
• Fuel in a Skid Tank
• Fuel in a 300 Gallon Skid Tank
• Fuel in a 550 Gallon Skid Tank
• Fuel in a 1000 Gallon Skid Tank
• Fuel in a 1500 Gallon Skid Tank
• Fuel in a 2000 Gallon Skid Tank
• Fuel in a 2500 Gallon Skid Tank
• Volume of a Torispherical Head
• Volume of a Torispherical Tank
• Hand Pump Volume: Computes the number of cycles (pumps or cranks) needed to move a specified volume
• Volume from Pump Rate over Time:  Computes gallons pumped or consumed based on a rate and time duration.