BIZOMAT 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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Inside diameter
- What it is
- The inside diameter of the cylindrical shell of the tank or vessel, which is also the diameter of its heads.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shell volume rises with the square of diameter and head volume with its cube.
- Get it right
- Use the inside diameter; the outside diameter overstates the volume by the wall thickness.
What this means: Straight shell length (tangent to tangent)
- What it is
- The length of the straight cylindrical part of the vessel, measured between the tangent lines where the heads begin.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shell volume rises in direct proportion; head volume does not change.
- Get it right
- Measure tangent to tangent, not the overall length including the heads.
What this means: Head type
- What it is
- The shape of the end closures from the vessel drawing: dished heads of different profiles, a cone or a flat plate.
- Units and format
- Choose one of 5 options from the list: 2:1 ellipsoidal; Hemispherical; Torispherical (ASME F&D, approximate); Conical; Flat.
- Example
- The form opens with “2:1 ellipsoidal” selected as a worked example. Choose the option that matches your case.
- Get it right
- Torispherical heads come in several proportions; the tool assumes one standard proportion, so treat it as approximate.
What this means: Number of heads
- What it is
- How many of the selected heads the vessel has: two for a closed vessel, one for a tank with a single dished end.
- Units and format
- Enter a number in heads: heads. The form accepts 0 heads to 2 heads. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 heads as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Total volume rises by one head volume for each extra head.
- Get it right
- A tank with one flat and one dished end needs one dished head here; a flat end adds no volume.
What this means: Cone half-angle (conical heads)
- What it is
- The angle between the cone surface and the vessel axis for a conical head. Used only when the head type is conical.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 89°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger half-angle gives a flatter, smaller cone and less head volume.
- Get it right
- This is the half-angle from the axis, not the included angle across the cone.
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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