KEVOS® MAKEOS · Geometry
Tank and Vessel Volume with Heads
What is the total volume of this vessel including its ends?
Volume of a cylindrical vessel with flat, 2:1 ellipsoidal, hemispherical, torispherical or conical ends, with the head and shell volumes shown separately.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Inside diameter | mm | Inside diameter of the shell. |
| Straight shell length (tangent to tangent) | mm | Length of the straight cylindrical part between head tangent lines. |
| Head type | choice | Head shape from the vessel drawing. |
| Number of heads | heads | 2 for a closed vessel, 1 for a vertical tank with one dished end. |
| Cone half-angle (conical heads) | ° | Half-angle of a conical head measured from the axis (conical heads only). |
Method and formulas
- Shell V = π D² L ÷ 4.
- Head volumes: 2:1 ellipsoidal π D³ ÷ 24; hemispherical π D³ ÷ 12; torispherical (crown radius D, knuckle 6% D) ≈ 0.0809 D³; conical π D³ ÷ (24 tan α); flat 0.
- Total = shell + number of heads × head volume.
- Example: 1000 mm × 2000 mm with two 2:1 ellipsoidal heads holds 1,832.6 L.
Limitations
- Inside dimensions; straight flanges of heads are counted in the shell length only if included there.
- The torispherical value is an approximation for standard flanged and dished proportions.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find capacity of a receiver, tank or hopper with dished ends
- Compare head types
- Estimate fill quantities
Who it is for
- Process engineers
- Fabrication estimators
- Maintenance planners
What you get
- Volume of each head
- Shell volume
- Total volume
Interpreting the result
- Use the head maker’s volume tables for exact capacities.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 68–69, 82–87. Topic reference; no source tables or recommended settings are reproduced.
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