Pipe wall thickness under internal pressure

What does this quantity describe?

For thin-walled pipes (da/di ≤ 1.7), the required minimum wall thickness tv = pe·da/(2·σallow·νN + pe) follows the same calculation approach used for welded pressure vessel shells. tv is explicitly defined without allowances or tolerances; the wall thickness actually ordered follows only from t = tv + c1 + c2, with the mill tolerance c1 and corrosion allowance c2.

Think of an inflated bicycle tube: a higher internal pressure or a larger diameter both require a thicker wall to avoid exceeding the same hoop stress, for a fixed allowable material stress.

Formula and variables

tv = pe · da / (2 · σzul · νN + pe)

• tv = pe · da / (2 · σallow · νN + pe)
• pe = 2 · σallow · νN · tv / (da − tv)
• σallow = (pe·da/tv − pe) / (2·νN)

Choose the inputs correctly

pe is the governing design pressure at design temperature, da the standardized pipe outside diameter, σallow the allowable (time-independent or time-dependent) stress of the pipe material at design temperature, and νN the weld joint factor (1.0 with full proof of weld soundness, 0.85 for spot inspection, 0.7 for visual inspection only).

How to use the calculator

Enter pe, da, σallow and νN to get tv. Then manually add c1 (mill undertolerance per pipe standard) and c2 (corrosion allowance) to determine the wall thickness to order.

Worked example

pe = 16 bar, da = 114.3 mm, σallow = 120 MPa and νN = 1 give tv = 1.6 MPa · 114.3 mm / (2·120 MPa·1 + 1.6 MPa) ≈ 0.76 mm.

Understand the result and units

tv ≈ 0.76 mm is the purely calculated wall thickness required from internal pressure alone, without any allowances. The wall thickness actually ordered is usually noticeably higher in practice, due to c1 and c2 as well as handling and stiffness considerations.

pe and σallow are often given in bar and MPa respectively, da and tv in mm; νN is dimensionless.

Why tv is not the wall thickness to order

Per DIN EN 13480-3, tv is explicitly defined as the calculated minimum wall thickness WITHOUT allowances or tolerances. The wall thickness actually ordered follows from t = tv + c1 + c2, where c1 is the allowable minus tolerance on pipe wall thickness per the relevant steel pipe standards (or alternatively expressed as a percentage c1' of the ordered thickness, typically 8% to 20%), and c2 is the corrosion or erosion allowance to be specified by the purchaser (usually 1 mm for ferritic steels, or 0 mm where no corrosion is expected). Forgetting these allowances results in ordering too thin a pipe wall.

Typical applications

The formula is used for the basic design of piping under internal pressure, e.g. in process engineering, plant construction and compressed-air or hydraulic lines, before further loads such as thermal expansion or self-weight are considered.

Assumptions, limits and common mistakes

The formula applies only to thin-walled, straight steel pipes with da/di ≤ 1.7 under predominantly static internal pressure. Thick-walled pipes require a different, nonlinear formula; thermal expansion, self-weight, vibration and pressure-cycle fatigue must be checked separately per DIN EN 13480-3.

Common mistake: A common mistake is using the calculated minimum wall thickness tv directly as the ordering thickness without adding the allowances c1 (manufacturing tolerance) and c2 (corrosion) — this understates the actually required pipe wall thickness.