Hydrostatic Testing

Barlow’s formula and percent SMYS, worked plainly

Almost every pressure decision on a pipeline runs through one relation between pressure, diameter and wall thickness. It is worth being fluent in it.

The relation

Hoop stress in a thin-walled cylinder is given by:

S = P D / 2t rearranged: P = 2 S t / D

where S is hoop stress, P is internal pressure, D is outside diameter and t is wall thickness. Consistent units throughout: psi and inches.

Turning stress into a test pressure

Specified minimum yield strength, SMYS, is a property of the pipe grade. Test pressures are usually expressed as a percentage of SMYS, because that is what bounds how hard you may push.

Substitute the target stress as a fraction of SMYS and the formula gives the pressure directly. A pipe tested to 90 percent SMYS is being loaded to 0.9 × SMYS in hoop stress, and Barlow tells you what pressure produces that in this particular diameter and wall.

The limits are regulatory, not just mechanical

What percentage you are allowed to reach depends on the medium and the class location. 49 CFR 192.503 sets the maximum hoop stress permitted during testing with a gas medium: for natural gas 80 percent in Class 1 and 30 percent in Classes 2, 3 and 4; for air or inert gas 80, 75, 50 and 40 percent respectively.

Those numbers are why medium selection and test pressure cannot be decided independently. Choosing air over water on a Class 3 line caps what you can prove.

Where it goes wrong

Using nominal wall where the segment contains a lighter wall run — the thinnest wall in the segment governs
Mixing outside and inside diameter
Forgetting that the pressure at the low point is the test pressure plus the static head, so the governing stress is not at the gauge
Applying one grade’s SMYS across a segment that contains more than one grade

The last two are the common ones on real profiles, and they are why segment breaks exist.

The rest of the arithmetic

Barlow rarely travels alone. Setting a test pressure also needs the elevation profile, the fill volume and the predicted pressure-temperature response.

The full set of relations and constants is published openly in the reference section of this site, and the same arithmetic is available in the HydroTech Pocket Engineer.

Standing noteThis is educational reference material, not engineering advice. Regulations are revised continually; the editions in force at the time of a project govern, and every project requires its own qualified engineering analysis and the operator’s governing specifications.

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