Vessel Head Volume Calculator

Estimate vessel head capacity with flexible inputs. Review types, levels, conversions, factors, and visual trends. Download clean reports for design checks and project records.

Advanced Calculator

Choose the geometric shape of the vessel end.
Use the internal diameter, not outside diameter.
Measured from crown or tip toward tangent line.
Use 2 for both ends of a closed vessel.
Water is about 1000 kg/m³.
Reset

Volume Curve

The graph shows filled volume as head height changes.

Sample curve shown

Example Data Table

Example Head type Inside diameter Head depth Filled height Approximate result
Process tank end 2:1 Ellipsoidal 2.00 m 0.50 m 0.50 m 1.0472 m³
Pressure vessel dome Hemispherical 1.50 m 0.75 m 0.75 m 0.8836 m³
Hopper style end Conical 1.20 m 0.40 m 0.25 m 0.0491 m³

Formula Used

Numerical slice method: V = ∫ πr(z)² dz

The calculator divides the head depth into thin slices. It finds the local radius at each slice. Then it integrates circular slice areas across the filled height.

2:1 ellipsoidal and hemispherical heads: r(z)² = R² × [1 - ((z - H) / H)²]. Here, R is the internal radius, and H is head depth.

Spherical cap and torispherical approximation: Rs = (R² + H²) / (2H). The cap radius is then calculated from the sphere profile. Torispherical heads use this as a practical approximation unless exact knuckle geometry is available.

Conical head: r(z) = R × z / H. The full conical head volume becomes V = πR²H / 3.

Mass estimate: Mass = Volume × Density. Weight force uses Weight = Mass × 9.80665.

How to Use This Calculator

  1. Select the vessel head type that matches your drawing.
  2. Enter the internal vessel diameter using one length unit.
  3. Enter head depth, or keep the standard depth checkbox selected.
  4. Enter a filled height. Leave it blank for a full head.
  5. Select the output volume unit and number of identical heads.
  6. Add liquid density when you also need mass and weight.
  7. Press calculate. The result appears above the form.
  8. Use CSV or PDF export to save the calculation record.

Vessel Head Volume in Design Work

Why Head Volume Matters

Vessel head volume is important in tank design and process checks. A head is the curved or tapered end of a vessel. It may store liquid, vapor, or both. The head shape affects the available capacity. It also affects level readings. A small change in fill height can change volume in a nonlinear way. This calculator helps by modeling common head profiles. It supports elliptical, hemispherical, spherical cap, conical, and approximate torispherical heads. It also converts units for quick review.

Where Engineers Use It

Engineers often need head volume during batching, calibration, and safety studies. A horizontal or vertical tank may include one or two heads. The liquid inside the head rarely behaves like a straight cylinder. Curvature makes the volume rise slowly near the crown. It rises faster near the tangent line. This is why a simple cylinder formula is not enough. The tool integrates thin slices across the head depth. Each slice uses the local radius. The method gives practical results for many planning tasks.

Choosing Good Inputs

The diameter should be the internal vessel diameter. The head depth should be the internal depth from crown to tangent line. Standard 2:1 elliptical heads often use one quarter of the diameter. Hemispherical heads use one half of the diameter. Custom heads may need measured values from drawings. If the drawing shows outside dimensions, subtract lining and wall thickness first. Better input data gives better volume estimates. The density field is useful when volume must be converted into mass.

Practical Notes

Use consistent units before comparing results. Mixed drawing notes can cause mistakes. Keep the same datum for fill height. Measure from the lowest crown point toward the tangent line. For partial filling, never enter a height larger than the head depth. The tool clamps that value.

Reports and Limitations

This page is designed for quick design checks. It can compare head types and liquid levels. It can also estimate total capacity for several identical heads. The chart shows how volume changes with fill height. CSV export helps with spreadsheets. PDF export helps with calculation records. Results are still estimates. Certified vessel work should use approved drawings, fabrication tolerances, and applicable design codes. Use the calculator as a fast engineering aid, not as a final document.

FAQs

1. What is vessel head volume?

It is the internal capacity inside a vessel end. The head may be elliptical, spherical, conical, or another curved shape.

2. Which diameter should I enter?

Enter the internal diameter. Outside diameter can overstate capacity because wall thickness and lining reduce usable volume.

3. What does standard depth mean?

It applies common depth ratios. A 2:1 elliptical head uses D/4. A hemispherical head uses D/2.

4. Can I calculate partial fill volume?

Yes. Enter the filled head height. Leave it blank when you want the full head volume.

5. Is the torispherical result exact?

It is an approximation. Exact torispherical volume needs dish radius, knuckle radius, and fabrication geometry.

6. Why does the chart curve bend?

Curved heads have changing radius with height. Volume growth is slower near the crown and faster near the tangent line.

7. How is liquid mass calculated?

The calculator multiplies filled volume by density. Use the correct liquid density for the expected temperature and mixture.

8. Can this replace certified vessel drawings?

No. It is for planning and checks. Use approved drawings and code requirements for final engineering decisions.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.