# Pressure Vessel(2:1 ellipsoidal head type) Volume Calculation

### Description

Volume calculation for:

- Horizontal pressure vessel with 2:1 ellipsoidal head type
- Vertical pressure vessel with 2:1 ellipsoidal head type
- Liquid volume

A horizontal pressure vessel with 2:1 ellipsoidal heads has a cylindrical section and two ellipsoidal heads at both ends. To calculate the total volume of the pressure vessel, you need to find the volume of the cylindrical section and the two ellipsoidal heads, then add them together.

- Cylindrical section volume: The volume of the cylindrical section (V_cylinder) can be calculated using the following formula:

V_cylinder = ? * (D/2)^2 * L

Where: D = diameter of the cylindrical section L = length of the cylindrical section

- 2:1 Ellipsoidal head volume: For each ellipsoidal head, the volume (V_head) can be calculated using the following formula:

V_head = (1/6) * ? * h * (3a^2 + h^2)

Since the heads are 2:1 ellipsoidal, the major axis (2a) is equal to the diameter of the cylindrical section (D), and the minor axis (h) is equal to D/2.

Thus, the formula becomes:

V_head = (1/6) * ? * (D/2) * (3(D/2)^2 + (D/2)^2)

- Total volume: The total volume of the horizontal pressure vessel (V_total) is the sum of the volumes of the cylindrical section and the two ellipsoidal heads:

V_total = V_cylinder + 2 * V_head

By combining the formulas for V_cylinder and V_head, you get:

V_total = ? * (D/2)^2 * L + (1/3) * ? * (D/2) * (3(D/2)^2 + (D/2)^2)

This formula can be used to calculate the total volume of a horizontal pressure vessel with 2:1 ellipsoidal heads. Note that this calculation assumes that the internal dimensions of the pressure vessel are used. If you need to calculate the volume based on external dimensions, you will need to account for the thickness of the vessel's walls.

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