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Test Analysis

Pressure–temperature analysis, and why half a degree decides the test

Pressure in a sealed, water-filled pipeline moves with temperature, air content and elastic effects whether or not a single drop leaks. The analyst’s job is to predict those movements so that what remains can be judged.

The relation

The predicted pressure change for a temperature change is:

ΔP = ΔT [ γ − 2(1 + ν)α ] ÷ [ (D/(Et))(1 − ν²) + C ]

The numerator is the competition between the water trying to expand and the steel trying to expand with it. The denominator is the system compliance: how much the pipe gives, plus how much the water compresses.

The constants, and the unit trap

  • Young’s modulus, steel: E = 29 × 10⁶ psi
  • Poisson’s ratio, steel: ν = 0.3
  • Linear expansion, steel: α = 6.5 × 10⁻⁶ per °F
  • Compressibility of water: C ≈ 3 × 10⁻⁶ per psi, temperature dependent
  • Volumetric expansion, water: γ ≈ 1.3 × 10⁻⁴ per °F near 68 °F
Match the unitsA Fahrenheit ΔT used with per-degree-Celsius coefficients overstates the predicted pressure change by a factor of 1.8. This is the single most common error in the analysis and it is large enough to turn a failing test into an apparently passing one.

Why water is not a constant

The volumetric expansion coefficient of water is strongly temperature dependent. Near 68 °F it is roughly 1.3 × 10⁻⁴ per °F. Near 39 °F it approaches zero, because that is where water reaches maximum density.

A test run on cold fill water in winter behaves very differently from the same test in summer, and using a summer coefficient on a winter test produces a prediction that is simply wrong.

The sensitivity is the point

For a typical transmission line the predicted response is on the order of tens of psi per degree Fahrenheit. Half a degree of unmeasured temperature drift is therefore comparable to the residual you are trying to detect.

This is why temperature instrumentation, its placement and its weighting are specified in the procedure rather than left to the crew, and why a single probe at the test head is not adequate on a long segment.

The balance statement

The output of the analysis is a balance: measured pressure change, minus predicted thermal response, equals unexplained residual. That residual is what acceptance is argued over.

A prediction made before the test, from measured fill volume and measured temperatures, is evidence. The same number produced afterwards to explain away a decay is not.

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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