The Formula and Where It Comes From
Barlow’s formula gives the internal pressure at which the wall of a pipe reaches a chosen stress S:
P = 2 × S × t / D
with P in the same pressure units as S, t = wall thickness and D = outside diameter. It falls straight out of the thin-wall hoop-stress relation (σθ = PD/2t): set the hoop stress equal to some limiting stress and solve for pressure. Every mill hydro test formula (P = 2St/D with S = 60–95% of yield) is Barlow in work clothes.
| Choosing S | What you get | Use case |
|---|---|---|
| S = SMYS (specified minimum yield) | Pressure at first yield of the wall | Line pipe hydro test factor basis (API 5L uses 85–95% of this) |
| S = design stress per code | Allowable working pressure | ASME B31.3: S = lesser of SMYS/1.5 or SMTS/3 (carbon steel, with quality factors on top) |
| S = ultimate tensile | Approximate burst pressure (order-of-magnitude) | Safety planning only — never a working number |
Barlow is a thin-wall formula: it assumes stress is uniform across the wall, which is only true when D/t is large (rule of thumb D/t ≥ 20). Thick-wall vessels need Lamé (thick-wall) equations — Barlow over-predicts strength as D/t falls.
Worked Examples You Can Check by Hand
Example 1 — yield pressure. API 5L X52 (SMYS 52,000 psi / 360 MPa), 8.625 in × 0.322 in (219.1 × 8.18 mm):
Pyield = 2 × 52,000 × 0.322 / 8.625 ≈ 3,884 psi (≈ 26.8 MPa)
Example 2 — allowable pressure, code style. Same pipe, B31.3-style S = 52,000/1.5 ≈ 34,667 psi, longitudinal ERW joint factor E = 1.0:
Pallow = 2 × 34,667 × 0.322 / 8.625 ≈ 2,589 psi (≈ 17.8 MPa)
Example 3 — GB/T-style mill test pressure. GB/T 8163 20# pipe (yield 245 MPa), 219.1 × 8.18, R = 0.6 × 245 = 147 MPa:
Ptest = 2 × 147 × 8.18 / 219.1 ≈ 11.0 MPa
Three legitimate numbers for one pipe: yield basis, code allowable, and mill test. Mixing them up — quoting a test pressure as a working pressure — is the most common self-inflicted error in procurement emails.
Where Barlow Stops Being Good Enough
- Thick walls (D/t < ~20): the stress distribution across the wall skews; Lamé gives the inner-fibre stress and the answer drops below Barlow. Hydraulic-cylinder barrels and heavy boiler headers live here.
- Welded pipe joint factors: some codes derate welded seams (historic factors: ERW/SAW now commonly 1.0 in API 5L, but older B31 practice derated furnace-weld and certain seams). Name the joint factor in any calculation.
- Corrosion and tolerance: design on minimum wall after corrosion allowance, not nominal. Barlow with nominal wall on a −12.5% tolerance spec overstates capability by 12.5%.
- Bending, supports, external loads: hoop stress is one term of several; B31 codes add bending, torsion, and pressure-design corrections (e.g. Y coefficients in B31.3’s own equation) — Barlow is a sanity check, not a substitute.
Quick reverse use: need the wall for a target pressure? Rearrange t = PD/2S and add corrosion allowance + tolerance margin. A 10 MPa working design on 219.1 mm with S = 138 MPa needs t ≈ 10 × 219.1 / (2 × 138) ≈ 7.9 mm → order 8.8 mm nominal on a −12.5% spec, or 8 mm on a tighter band.
Frequently Asked Questions
Is Barlow’s formula code-legal for design?
As a communication tool, yes; for code work, use the code’s own equation (ASME B31.3 §304.1.2 includes thickness and Y-factor corrections). Barlow matches its results closely for thin walls and is excellent for sanity checks.
Why does my supplier’s test pressure differ from my Barlow number?
Different S: mills test at a defined fraction of yield (60–95% by standard), while your number may be yield-based or allowable-based. Ask which factor was used.
Does OD or ID go in the formula?
Barlow uses outside diameter with wall measured from OD (the pipe convention). Versions with mean diameter exist — consistency matters more than the 1–2% difference.
Can I use Barlow for external pressure?
No. External pressure failures are buckling, governed by a different set of equations (B31.3/B31.8 external pressure chapters, or NV codes).
How does temperature change the number?
Strength falls with temperature — use the design stress at design temperature (code tables), and remember pressure ratings of flanges fall faster than pipe wall capability.
Standards & references: ASTM A530 · ASME B31.3 · API 5L
Not sure which tolerance or size class to order? CREATEEL exports carbon steel welded and seamless pipe to API, ASTM, EN and GB standards — send us the drawing and duty, we quote the right class. Get a quote.
