KEVOS® MAKEOS · Strength
Spherical Pressure Vessel Design (Thickness, Stress, Capacity, Hydrotest)
How thick must this spherical vessel be for its pressure, what stress and safety factor does the chosen plate give after corrosion, what does it hold and weigh, and is the hydrotest within limits?
Design of a spherical shell under internal pressure: thin-wall membrane stress and the thick-wall maximum stress at the bore (as the spherical shell tool) with the thickness reduced by the corrosion allowance, the safety factor on yield, the least thickness for the required factor plus allowance, capacity and shell mass, and the stress at the hydrotest pressure against your share of yield.
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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 sphere. |
| Plate thickness | mm | Nominal plate thickness. |
| Corrosion allowance | mm | Corrosion allowance taken off the thickness for the stress check. |
| Design pressure | MPa | Internal design pressure. |
| Yield strength | MPa | Yield strength of the plate at temperature. |
| Safety factor on yield required | Safety factor on yield you require (code design uses allowable stresses instead; this is a screening check). | |
| Hydrotest pressure ÷ design pressure | Hydrotest pressure as a multiple of the design pressure (from your code). | |
| Largest hydrotest stress as a share of yield | % | Largest membrane stress during the hydrotest as a share of yield (your value). |
| Plate density | kg/m³ | Density of the plate. |
Method and formulas
- Thin wall σ = p d_i ÷ 4t; thick wall maximum σ = p (r_o³ + 2r_i³) ÷ [2(r_o³ − r_i³)] (as the spherical shell tool), with t reduced by the corrosion allowance.
- Safety factor = S_y ÷ maximum stress; thickness needed = p d_i × factor ÷ (4 S_y) + allowance.
- Capacity = π d_i³ ÷ 6; shell mass = ρ π (d_o³ − d_i³) ÷ 6; hydrotest stress = membrane stress × hydrotest ratio.
- Example: 6 mm plate (5 mm after allowance) runs at 60.011 MPa, a factor of 4.1659; the sphere holds 113.1 L and weighs 54.341 kg.
Limitations
- Membrane region only; nozzles, supports and welds need code design.
- Pressure vessels must be designed and certified to the applicable code.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a spherical gas receiver or tank
- Compare a sphere with a cylinder for the same volume
- Check a sphere for a hydrotest
Who it is for
- Mechanical engineers
- Design engineers
- Inspection engineers
What you get
- Membrane and maximum stress, safety factor
- Thickness needed with allowance
- Capacity, shell mass and hydrotest stress
Interpreting the result
- A sphere needs about half the wall of a cylinder of the same diameter and pressure.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294. Topic reference; no source tables or recommended settings are reproduced.
WORKOS 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 Spherical Pressure Vessel Design (Thickness, Stress, Capacity, Hydrotest) calculator
