BIZOMAT MAKEOS · Strength
Pressure Vessel Shell Plan (Required Thickness, Plate Chosen, MAWP, Test Water)
For a cylindrical pressure vessel with 2:1 ellipsoidal heads, what thickness is needed, what working pressure does the plate I have allow, and how much water does the hydrostatic test take?
Plan of a cylindrical pressure vessel shell and heads: the required thickness of the shell and of 2:1 ellipsoidal heads with joint efficiency and corrosion allowance and the hydrostatic test pressure (as the pressure vessel thickness tool), then the maximum allowable working pressure of the plate you choose for both, the volume and water mass for the hydrostatic test, and the mass of the shell course.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Design pressure | MPa | Internal design pressure. |
| Inside diameter | mm | Inside diameter of the shell. |
| Allowable stress at design temperature | MPa | Allowable stress of the plate at the design temperature, from your pressure vessel code. |
| Joint efficiency | Efficiency of the longitudinal weld from the code and the extent of radiography. | |
| Corrosion allowance | mm | Thickness allowed for corrosion over the vessel’s life. |
| Hydrotest factor | Hydrostatic test pressure as a multiple of design pressure, from your code. | |
| Plate and size | ||
| Plate thickness chosen (shell and heads) | mm | Nominal thickness of the plate you will use for the shell and heads (after forming thinning). |
| Shell length (tangent to tangent) | mm | Length of the cylindrical shell between the head tangent lines. |
| Plate density | kg/m³ | Density of the plate (7850 for steel). |
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: Design pressure
- What it is
- The internal pressure the vessel is designed for, above atmospheric, from the process data or design specification. Shell and head thickness are worked from it.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Required thickness rises roughly in proportion to the design pressure.
- Get it right
- Use gauge pressure in MPa (1 MPa = 10 bar), not absolute pressure.
What this means: Inside diameter
- What it is
- The inside diameter of the cylindrical shell. It sets the thickness, the volume for the hydrostatic test and the shell course mass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20000 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
- Required thickness rises roughly in proportion to the diameter.
- Get it right
- Use the inside diameter, not the outside; the formulas are written for the inside size.
What this means: Allowable stress at design temperature
- What it is
- The allowable stress of the plate material at the design temperature, taken from your pressure vessel code’s stress tables.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 1000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 138 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher allowable stress lowers the required thickness and raises the MAWP.
- Get it right
- Use the code value at the design temperature, not the yield or tensile strength of the plate.
What this means: Joint efficiency
- What it is
- The efficiency of the longitudinal weld seam, set by your pressure vessel code from the joint type and the extent of radiography.
- Units and format
- Enter a plain number with no unit. The form accepts 0.3 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.85 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower joint efficiency raises the required thickness and lowers the MAWP.
- Get it right
- Enter it as a decimal, not a percentage: a fully efficient joint is 1, not 100.
What this means: Corrosion allowance
- What it is
- The extra thickness added for metal expected to be lost to corrosion or erosion over the vessel’s life, from the process conditions or your specification.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It adds directly to the required thickness and reduces the plate available for pressure.
- Get it right
- Use 0 only if the code and service allow no allowance; it is added to both shell and heads.
What this means: Hydrotest factor
- What it is
- The hydrostatic test pressure as a multiple of the design pressure, taken from your pressure vessel code.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The test pressure rises in direct proportion to the factor.
- Get it right
- Some codes also correct the test pressure for the stress ratio at test and design temperatures; check your code.
Plate and size
What this means: Plate thickness chosen (shell and heads)
- What it is
- The plate thickness you intend to use for both the shell and the heads, after any thinning in forming. It is compared with the thickness needed and gives the MAWP.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker plate raises the MAWP of both shell and heads.
- Get it right
- Use the minimum thickness after forming and mill tolerance, not the ordered nominal plate.
What this means: Shell length (tangent to tangent)
- What it is
- The length of the cylindrical shell between the tangent lines where the heads begin. It sets the shell volume and the shell course mass.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Test water volume and shell mass rise with the length.
- Get it right
- Measure between tangent lines, not the overall length including the heads.
What this means: Plate density
- What it is
- The density of the plate material, from the material data sheet. It turns the shell course volume into mass.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shell course mass rises in direct proportion to density.
- Get it right
- Enter it in kg/m³; a value in g/cm³ must be multiplied by 1000.
Method and formulas
- Shell t = P R ÷ (S E − 0.6P) + CA; 2:1 ellipsoidal head t = P D ÷ (2S E − 0.2P) + CA; test pressure = factor × P (as the pressure vessel thickness tool).
- MAWP of the shell = S E t_c ÷ (R + 0.6 t_c); of the head = 2 S E t_c ÷ (D + 0.2 t_c), with t_c = chosen − CA.
- Volume = π D² L ÷ 4 + 2 × π D³ ÷ 24; shell mass = π (D + t) t L ρ.
- Example: the shell needs 5.7845 mm; 8 mm plate allows 1.5131 MPa; the test takes 2,618 kg of water.
Limitations
- Internal pressure only; external pressure, nozzles, supports and wind need the full code design.
- Head thickness is the finished thickness after forming.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Pick a plate thickness for an air receiver or tank
- Find the working pressure of an existing shell
- Plan the water for a hydrostatic test
Who it is for
- Pressure vessel designers
- Fabrication engineers
- Inspectors
What you get
- Thickness needed for shell and heads, and test pressure
- Working pressure of the chosen plate
- Test water and shell mass
Interpreting the result
- The heads of a 2:1 ellipsoidal design need about the same thickness as the shell, so one plate thickness often serves both.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Remaining life and inspection intervals
In Ultrasonic Testing by the Numbers
What it covers: From survey readings to a decision: minimum required thickness for pipe and vessel shells, corrosion rate, remaining life, its uncertainty, the next inspection date and when to repair or replace.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Pressure Vessel Shell Plan (Required Thickness, Plate Chosen, MAWP, Test Water) calculator