Table of Contents
In Chemical Engineering, vessels like reactors, storage tanks, and mixing tanks are used to handle fluids, gases, or solids under controlled conditions, and calculating vessel volume is key to ensuring proper capacity, efficient mixing, heat and mass transfer, and safe operation under pressure and temperature limits.
ChemEnggCalc has developed a ready-to-use Vessel Volume Calculator tool that instantly calculates the volume and filling percentage for various head types – including ellipsoidal, hemispherical, torispherical, flat, and custom – in both horizontal and vertical orientations.
Vessel Volume Calculator
This ChemEnggCalc Vessel Volume Calculator is a web-based tool used to calculate the total and filled volumes of vessels with various head types (ellipsoidal, hemispherical, torispherical, flat, or custom) in horizontal or vertical orientations.
Users input parameters like diameter, straight length, liquid level, and head-specific dimensions, and this tool computes volumes in cubic meters, displays a fill percentage, and generates a calibration table. It also features a visual vessel diagram and allows PDF export of results.
Related: Area of Cross-Section Calculator for Hollow Sections, Beams & Shapes
Related: Friction Factor Calculator Moody’s Diagram for Smooth and Rough Pipes
Types of Vessel Heads
Vessel Heads (also called end caps) are the curved or flat ends of pressure vessels and storage tanks. These are designed based on process requirements such as pressure, temperature, fluid properties, and ease of cleaning. Here, we’ve provided the different types of vessel heads commonly used in chemical engineering design.
Vessel volume plays an important role in equipment design, as it determines capacity, ensures adequate residence time, supports efficient mixing and heat transfer, and contributes to safe and cost-effective operation.
Must Read: Personal Carbon Footprint Calculator – Track your CO2 Emissions
Related: Critical Thickness of Insulation Calculator for Cylinder and Sphere
The table is based on the head types available in the calculator: ellipsoidal, hemispherical, torispherical (ASME F&D, Standard F&D, 80:10 F&D), flat, and custom (conical approximation).
| Head Type | Description | Uses |
|---|---|---|
| Ellipsoidal (2:1 Elliptical) | A head with an elliptical shape where the major axis is twice the minor axis (depth = D/4). | Commonly used in pressure vessels due to its balance of strength and material efficiency. Ideal for medium- to high-pressure applications in chemical processing, oil and gas, and pharmaceutical industries. |
| Hemispherical | A head shaped like half a sphere (depth = D/2). | Used in high-pressure vessels (e.g., reactors, storage tanks) due to its superior strength and uniform stress distribution. Common in petrochemical, nuclear, and high-pressure gas storage applications. |
| Torispherical (ASME F&D) | A head with a dish radius equal to the vessel diameter (f=1) and a knuckle radius of 6% of the diameter (k=0.06). | Widely used in pressure vessels for moderate pressures in chemical, food processing, and water treatment industries. Offers a cost-effective alternative to hemispherical heads. |
| Torispherical (Standard F&D) | Similar to ASME F&D but with a knuckle radius of 10% of the diameter (k=0.1). | Used in general-purpose pressure vessels and storage tanks in industries like chemical processing and HVAC systems, where moderate pressure and cost savings are priorities. |
| Torispherical (80:10 F&D) | A head with a dish radius of 80% of the diameter (f=0.8) and a knuckle radius of 10% (k=0.1). | Used in specialized applications requiring a shallower head than standard F&D, such as in certain chemical reactors or tanks with space constraints. |
| Flat | A flat plate used as the vessel end. | Used in low-pressure or non-pressure vessels, such as storage tanks for liquids at atmospheric pressure (e.g., water, food products). Simple and cost-effective but limited to low-pressure applications. |
| Custom (Conical Approx.) | A user-defined head approximated as a conical shape with specified dish depth (a). | Used in specialized vessels where custom head shapes (e.g., conical or near-conical) are required, such as in certain chemical reactors, hoppers, or vessels with unique process needs |
Vessel Volume Formula
Vessel volume refers to the internal capacity of the vessel, which includes the cylindrical body and the heads at both ends. The total volume of vessel is calculated as:
\[V_{\text{total}} = \frac{\pi D^2 L}{4} + 2 \cdot V_{\text{head}}\]
where,
- Vtotal is the total volume of the vessel
- Vhead is the volume of one head, which varies depending on the head type
- D is the diameter of the vessel
- L is the straight length of the cylindrical section
The table below provides the vessel volume formulas for different head types.
| Head Type | Vhead Formula | Total Vessel Volume Formula |
|---|---|---|
| Ellipsoidal (2:1) | π D³ / 96 | π D² L / 4 + 2 * (π D³ / 96) |
| Hemispherical | π D³ / 12 | π D² L / 4 + 2 * (π D³ / 12) |
| Torispherical (ASME F&D) | 0.0847 D³ | π D² L / 4 + 2 * (0.0847 D³) |
| Torispherical (Standard F&D) | 0.0808 D³ | π D² L / 4 + 2 * (0.0808 D³) |
| Torispherical (80:10 F&D) | 0.0746 D³ | π D² L / 4 + 2 * (0.0746 D³) |
| Flat | 0 | π D² L / 4 |
| Custom (Conical Approx.) | π D² a / 6 | π D² L / 4 + 2 * (π D² a / 6) |
Also Read: Chemical Engineering as a career option in India
Related: Centrifugal Pump Sizing Calculation – TDH, NPSHa vs Flow Rate curve & Power Required
Resources
- Pressure Vessel Design Manual
- CRC Handbook of Chemistry and Physics” by David R. Lide
- Perry’s Chemical Engineers’ Handbook“ by Don W. Green and Marylee Z. Southard
- “Transport Processes and Unit Operations“ by Christie J. Geankoplis
Disclaimer: The content provided here is for educational purposes. While efforts ensure accuracy, results may not always reflect real-world scenarios. Verify results with other sources and consult professionals for critical applications. Contact us for any suggestions or corrections.
