Required wall thickness for cylindrical shells, spherical shells, hemispherical heads and 2:1 ellipsoidal heads under internal pressure. Returns nominal plate thickness, hoop and longitudinal stress in the corroded condition, and maximum allowable working pressure.
All four cases use the thin-shell membrane equations of ASME Section VIII Division 1. The corrosion allowance is added after the pressure calculation, and stress and MAWP are then checked on the corroded thickness — the condition the vessel must still be safe in at the end of its life.
P internal design pressure (MPa) ·
R inside radius (mm) ·
D inside diameter (mm) ·
S maximum allowable stress (MPa) ·
E joint efficiency ·
CA corrosion allowance (mm) ·
tnet corroded thickness (mm)
A carbon steel cylindrical vessel, 1500 mm inside diameter, designed for 10 bar at 150 °C, spot radiographed, with 3 mm corrosion allowance.
The vessel is adequate but tight — MAWP exceeds design pressure by only 1 %. Moving to full radiography (E = 1.00) would drop the required thickness to 5.46 mm and allow the same 9.5 mm plate to carry a considerably higher MAWP, which is often worth the inspection cost.
| Quantity | Symbol | Unit | Accepted range |
|---|---|---|---|
| Design pressure | P | bar, MPa or psi | > 0 |
| Inside diameter | D | mm or in | > 0 |
| Allowable stress | S | MPa | > 0 |
| Joint efficiency | E | dimensionless | 0.1 – 1.0 |
| Corrosion allowance | CA | mm | ≥ 0 |
| Design temperature | T | °C or °F | any |
| Required thickness | t | mm | output |
| Nominal plate | tnominal | mm | output |
| MAWP | — | bar | output |
Pressure is converted to MPa internally: 1 bar = 0.1 MPa and 1 psi = 0.00689476 MPa. Diameters in inches are converted at 25.4 mm. The ASME minimum shell thickness of 1.5875 mm (1/16 in) is applied as a floor.
| Examination | E | Effect on thickness |
|---|---|---|
| Full radiography | 1.00 | Thinnest plate, highest inspection cost |
| Spot radiography | 0.85 | Common compromise |
| No radiography | 0.70 | Roughly 43 % more plate than full RT |
| Material | S (MPa) | Typical use |
|---|---|---|
| Carbon steel | 138 | General pressure vessel plate |
| Stainless 304 | 138 | Corrosion service, food and pharma |
| Stainless 316 | 115 | Chloride and acid service |
For a cylindrical shell under internal pressure ASME Section VIII Division 1 paragraph UG-27 gives t = P·R / (S·E − 0.6P), where P is internal design pressure, R is the inside radius, S is the maximum allowable stress and E is the joint efficiency. The corrosion allowance is added afterwards, and the result is rounded up to an available plate thickness.
Joint efficiency accounts for the reliability of welded seams and the extent of radiographic examination. Under ASME Section VIII Division 1 Table UW-12 a double-welded butt joint with full radiography takes 1.00, with spot radiography 0.85, and with no radiography 0.70. Lower joint efficiency directly increases the required thickness, so the cost of radiography is often offset by the saving in plate.
Typical corrosion allowance is 1.5 to 3 mm for carbon steel in general service, and 3 to 6 mm in corrosive duty. Stainless steel and clad vessels often carry zero or a nominal allowance. The allowance is added to the calculated thickness before rounding up to plate size, and it is subtracted again when checking stress and maximum allowable working pressure in the fully corroded condition.
Maximum allowable working pressure is the highest pressure the vessel may carry in its corroded condition at design temperature, based on the thickness actually installed. Design pressure is the value the vessel was specified to. Because nominal plate is always thicker than the calculated requirement, MAWP is normally somewhat higher than design pressure, and it is MAWP that sets the relief valve pressure.
The UG-27 membrane formulas assume a thin shell where stress is essentially uniform through the wall. They apply while thickness does not exceed half the inside radius, or equivalently while pressure does not exceed 0.385·S·E. Beyond that the through-wall stress gradient becomes significant and the thick-wall rules of ASME Section VIII Division 1 Appendix 1-2 or Division 2 must be used instead.