EngCalc

Method

How the calculator gets from two sets of readings to a leak rate at reference conditions and its expanded uncertainty: the pressure-change method, with uncertainty propagated to first order as described in the GUM.
Open the calculator
1

Absolute pressures

Each reading is a gauge pressure plus the barometric pressure at that moment. Temperatures are absolute (K or °R).
2

Leak rate at reference conditions

In a closed, rigid enclosure the amount of gas is proportional to P/T. Its change over the interval, scaled by V/Δt and expressed at the reference state, is the leak rate. Positive Q means gas entered.
3

Sensitivity coefficients

How strongly Q responds to each measured quantity: the partial derivatives of Q.
4

Combined standard uncertainty

The law of propagation of uncertainty for uncorrelated inputs: the root sum of squares of each sensitivity times the standard uncertainty of its reading. Each term’s square, as a share of the total, is the budget shown with the result.
over P₁, P₂, T₁, T₂ and Δt; each uᵢ is the standard uncertainty you entered for that reading
5

Simplified method

If the pressure and temperature barely change (P₁ ≈ P₂, T₁ ≈ T₂) and the timing term is negligible, the budget collapses to a closed form. It is shown alongside the full method and flagged when its assumptions don’t hold.
6

Expanded uncertainty

The coverage factor k is the two-sided Student-t quantile for the confidence level, with infinite degrees of freedom (the normal distribution) unless you choose otherwise. The result is reported as Q ± U.
the leak rate as a fraction of the enclosure volume per hour

Assumptions

The enclosure is rigid and closed: its volume does not change during the test.
The gas behaves as an ideal gas over the test range.
Temperatures are representative of the gas inside the enclosure and are absolute (K or °R).
The pressure and temperature readings are uncorrelated, with the same standard uncertainty at the start and the end.

Limitations

No correction for water-vapour content, gas composition changes or gas solubility.
The volume, the reference conditions and the barometric readings are treated as exact; their uncertainties are not in the budget.
Not a substitute for the acceptance criteria of the test procedure or standard you work to.

References

Method note “Leak rate formula and uncertainty calculation”, with its worked example (pressure decay of a 60 ft³ glovebox).
JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM).
§5.1 (law of propagation of uncertainty), §6 (expanded uncertainty)