A pressure test proves the integrity of a completed pressure boundary by taking it above its working pressure under controlled conditions. The margin above MAWP is deliberate: it demonstrates that the joint efficiency assumed in design is real, exposes gross workmanship defects and leak paths, and produces a small amount of local yielding at stress concentrations that redistributes residual stress.

The stress ratio is the part most often missed. Codes require the test factor to be multiplied by the ratio of the allowable stress at test temperature to the allowable stress at design temperature. A vessel designed for 400 °C has a much lower allowable stress at temperature than at the ambient temperature it is tested at, so a bare 1.3 × MAWP test would not develop the intended fraction of the design margin. ASME VIII-1 UG-99(b) requires 1.3 × MAWP × (S_test/S_design) using the lowest ratio for any material in the vessel. ASME B31.3 §345.4.2 uses 1.5 × design pressure with the same ratio, capped at 6.5.

Pneumatic testing is different and more dangerous. Water is nearly incompressible, so a hydrostatic failure releases very little stored energy — the pressure collapses as soon as the boundary opens. A gas-filled vessel stores enormous energy and fails explosively. Because of that, codes set a lower factor for pneumatic tests (1.1 in ASME VIII-1 UG-100 and B31.3 §345.5) and require additional precautions: exclusion zones, remote monitoring, a stepped pressurisation with holds, and a documented justification for why a hydrostatic test cannot be used.

The test pressure must also be checked against yield. A test that puts the shell close to its yield strength risks gross distortion, particularly at nozzles and other stress raisers, and B31.3 permits the test pressure to be reduced where it would produce a stress in excess of yield at test temperature. Finally, remember that the pressure at the bottom of a tall vertical vessel is the gauge test pressure plus the static head of the test water — around 0.098 bar per metre — and it is the bottom course, not the gauge, that sees the highest stress.

Worked example

MAWP or design pressure	5 MPa
Governing code and test type	asme_viii_hydro
Allowable stress at test temperature	138 MPa
Allowable stress at design temperature	118 MPa
Outside diameter	508 mm
Wall thickness	12.7 mm
Specified minimum yield strength	240 MPa
Static head above the gauge	0 m
Weld joint efficiency	1
Effective code test factor	1.3
Stress ratio S_test / S_design	1.169
Stress ratio applied	1.169
Test pressure at the gauge	7.6 MPa
Test pressure including static head	7.6 MPa
Hoop stress at test pressure	148.99 MPa
Hoop stress as a fraction of SMYS	62.1 %

Stress ratio = 138/118 = 1.169492. UG-99(b): P_T = 1.3 x 5.0 x 1.169492 = 7.6017 -> 7.60 MPa. Hoop stress at test: R = 254 - 12.7 = 241.3 mm, so sigma = 7.6017 x (241.3 + 0.6x12.7)/(12.7 x 1.0) = 7.6017 x 248.92/12.7 = 7.6017 x 19.60 = 148.993 -> 148.99 MPa. That is 148.99/240 = 62.1 % of SMYS, comfortably below yield. With no static head the pressure at the bottom equals the gauge pressure.

Use at your own risk — verify before you act

These calculators support, and never replace, the judgement of qualified NDT and engineering personnel. Results are provided as is, without warranty of any kind, express or implied, and must be independently verified against the governing code edition named in your contract before being used in any inspection, acceptance, rejection, radiation-safety or fitness-for-service decision. By using them you accept full responsibility for how the results are applied; NDT Inspect, its owners and contributors accept no liability for any loss, damage, injury or death arising from their use or from reliance on them. If a result matters to safety, check it by hand and have it reviewed by a competent person.