Flow Measurement · Glossary

What is Expansibility Factor?

Symbol: εdimensionless, 1 for liquidsFlow Measurement

Expansibility factor corrects DP flow equations for the drop in gas density as gas expands through the flow element.

Expansibility Factor Explained

Liquids are almost incompressible, so ε = 1. Gas and steam expand as pressure falls through the restriction, so the flow is slightly less than the incompressible equation predicts.

The effect grows with the ratio of DP to static pressure. Keeping DP small relative to line pressure keeps ε close to 1.

Expansibility Factor Formula

ε = 1 − (0.351 + 0.256 β⁴ + 0.93 β⁸) × [1 − (p₂ ÷ p₁)^1/κ]

β	beta ratio
p₁, p₂	upstream and downstream absolute pressure
κ	isentropic exponent

Note: Orifice plate formula from ISO 5167-2:2003, valid for p₂ ÷ p₁ ≥ 0.75.

Calculators for Expansibility Factor

CalculatorOrifice Flow CalculatorFree online calculator with formula and worked example.CalculatorDP Flow Measurement Uncertainty Calculator (ISO 5167-1)Free online calculator with formula and worked example.

Frequently Asked Questions

What is Expansibility Factor?

Expansibility factor corrects DP flow equations for the drop in gas density as gas expands through the flow element.

Is ε needed for steam?

Yes. Steam is a compressible fluid, so ε applies just as for gas.

What is a typical value?

Usually between about 0.97 and 1 for gas meters designed with modest DP.

Learn more on the blog

Mistakes in DP flow measurement

A practical guide on instrumentationblog.in with more detail on expansibility factor and how it is applied on real plants.

Read Full Article

More Flow Measurement Terms

Flow termVena ContractaVena contracta is the point just downstream of an orifice where the jet is narrowest and the pressure is…Flow termPermanent Pressure LossPermanent pressure loss is the part of the DP across a flow element that is not recovered downstream and…Flow termSquare Root ExtractionSquare root extraction converts a DP signal into a linear flow signal, because flow through a DP element…Flow termTurndown RatioTurndown ratio is the maximum flow divided by the minimum flow a meter can measure within its stated accuracy.Flow termLow Flow CutoffLow flow cutoff forces the flow reading to zero below a set value, so noise and zero drift do not show as…Flow termK FactorK factor is the number of pulses a flow meter sends for each unit volume of fluid passing through it.

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