Pipeline hydrotest: hoop stress
Hoop stress and its percentage of SMYS at the test pressure — at the gauge and at the lowest point of the section, where the water column adds to the pressure.
P_low = P_test + ρ_w · g · Δzσ_h = P · D / (2 · t)σ_h / SMYS · 100 %The test pressure comes from the design: at least 1.25 times the design pressure for 4 h under ASME B31.4, by location class under B31.8. The test stress is usually limited to 90–100 % SMYS at the lowest point, while the highest point must still see the required pressure. Barlow's formula with the outside diameter is conservative.
Source: Barlow's formula; ASME B31.4, para. 437.4.1; ASME B31.8, para. 841.3
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Gauge pressure where the gauge is installed.
0 if the gauge is at the lowest point.
Nominal; for a strict check subtract the mill under-tolerance.
From the line pipe specification or the mill certificate.
Unit converter for this formulaPressure · Length · Density and °API · Fraction and percent
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- σ_h — Hoop stress at the lowest point–
- P_low — Pressure at the lowest point–
- σ_g — Hoop stress at the gauge, % SMYS–
- P_100 — Pressure giving a hoop stress equal to SMYS–
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Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.