When gas flows through an orifice plate its pressure drops, and because gas is compressible its density drops with that pressure, so the gas leaving the bore is less dense than the gas that entered. An orifice flow equation that ignored this would treat the gas as if its density stayed fixed across the plate and would compute the wrong flow. The expansibility factor, written epsilon in ISO 5167, is the correction that accounts for that density change. It is the ISO 5167 counterpart to the expansion factor written Y in AGA 3, describing the same physical effect with the same purpose, and it is applied as a multiplier in the flow equation. This guide explains what drives epsilon, why it collapses to one for liquids, and how a flow computer that hardcodes or mis-signs it quietly under-reports gas volume when the differential pressure is high.
Expansibility Factor in one line: The expansibility factor, epsilon in ISO 5167, is a dimensionless correction applied to the orifice flow equation to account for the drop in gas density as the gas expands through the pressure drop across the plate. It is the ISO 5167 name for the same quantity AGA 3 calls the expansion factor Y. Epsilon is always less than or equal to one, and it moves further below one as the ratio of differential pressure to upstream pressure grows and as the gas becomes more compressible, so it matters most at high differential and least for a light, low-pressure-drop stream. For an incompressible liquid the density does not change across the plate and epsilon equals exactly one.
The core orifice flow equation relates the mass or volume flow to the square root of the differential pressure, the bore area, the discharge coefficient, and the density of the fluid. The subtlety is which density to use, because the gas is denser upstream of the plate than in the throat where it has expanded. Rather than track a varying density through the constriction, ISO 5167 uses the upstream density and applies the expansibility factor epsilon as a single multiplier that folds in the effect of the expansion. Epsilon is therefore not a separate physical measurement but a computed correction, derived from an empirical equation that the standard specifies, that adjusts the idealized incompressible result into the correct compressible one.
Two ratios drive the value of epsilon. The first is the ratio of the differential pressure to the absolute upstream pressure, sometimes called the pressure ratio across the plate. A large differential relative to the line pressure means the gas expands a great deal as it crosses the orifice, so the density change is large and epsilon sits well below one. A small differential on a high line pressure means the gas barely expands, so epsilon is close to one. The second driver is the isentropic exponent of the gas, a property tied to how the gas stores energy, which governs how much the density falls for a given pressure drop. A gas with a lower isentropic exponent expands more for the same pressure ratio, pushing epsilon lower.
Beta ratio enters the empirical epsilon equation as well, because the geometry of the constriction affects the expansion, but the dominant lever is almost always the pressure ratio. What matters operationally is the direction and the magnitude: epsilon is always at or below one, and it departs from one increasingly as the differential pressure climbs relative to the line pressure. On a low-differential meter epsilon might be so close to one that neglecting it would introduce only a tiny error, but on a high-differential meter it can pull the flow down by a percentage that is far from negligible for custody purposes, which is exactly why the standard insists it be computed rather than assumed.
For a liquid the whole correction disappears, and understanding why makes the concept concrete. Liquids are effectively incompressible over the pressure drop of an orifice meter, meaning their density does not change measurably as they cross the plate. If the density is the same upstream and in the throat, there is no expansion effect to correct for, and the expansibility factor is exactly one by definition. A liquid orifice calculation simply omits epsilon, or equivalently carries it as unity, because there is nothing for it to do. This is a useful sanity check: any nonzero departure of epsilon from one is entirely a compressible-gas phenomenon, so seeing epsilon at one on a stream you believe is gas is a sign something is misconfigured.
The relationship to AGA 3's expansion factor Y is that they describe the same effect and behave the same way, both starting at one and falling as the pressure ratio grows, but they are defined by their own respective standards with their own empirical equations. In practice the numerical values are very close for the same conditions because the underlying physics is identical, but a calculation nominally following ISO 5167 must use the ISO 5167 epsilon equation, and one following AGA 3 must use the AGA 3 Y equation, so that the correction is consistent with the discharge coefficient and reference basis it is paired with. Mixing an epsilon from one standard into an equation set from the other is a subtle configuration error that a careful measurement review looks for.
There is also a directional convention that has to be right. Epsilon is normally computed using the upstream pressure and the upstream density, because the flow equation is written around the upstream tap. If a flow computer were configured to reference the wrong tap, or to take the pressure ratio with an inverted sign, the correction would move in the wrong direction and the error would grow precisely when it matters most. Because epsilon is a small correction near one, a sign or reference mistake in it produces a bias that is easy to overlook on a spot check yet consistent enough to distort a monthly volume, which is why its configuration deserves explicit verification rather than trust.
The failure that a measurement team most wants to catch is a flow computer that hardcodes epsilon to one, or freezes it at a value chosen for one operating point, instead of computing it live from the current pressure ratio and gas properties. Because epsilon is always at or below one, forcing it to one over-multiplies the flow, but the more common practical error is subtler: on a meter that swings between low and high differential, a fixed epsilon is right at the point it was set and wrong everywhere else. When the differential climbs, the true epsilon falls further below the frozen value, and the flow computer, still using the stale number, computes a flow that is biased relative to the correct compressible result. The bias grows exactly with the differential, so it concentrates during high-rate periods that carry the most volume.
Surfacing epsilon as a live value in SCADA turns this hidden configuration issue into something observable. A cloud platform such as Merobix can carry the computed expansibility factor alongside the differential pressure, the line pressure, and the flow, so a measurement engineer can see whether epsilon actually moves as the differential moves. A healthy gas meter shows epsilon tracking below one and dipping further as differential rises; a meter whose epsilon sits flat at exactly one regardless of differential is almost certainly not applying the correction, and a meter whose epsilon moves the wrong way as differential rises has a sign or reference problem. None of these are visible from the flow reading alone, but all of them stand out immediately when epsilon itself is trended.
Keeping epsilon visible also supports the audit trail that custody measurement requires. The whole point of the expansibility correction is that the reported volume should reflect the real compressible behavior of the gas at each interval's actual conditions, so the record should show that epsilon was computed from those conditions rather than assumed. When the platform stores the epsilon used per interval alongside the pressures and the flow, an auditor can confirm the correction was applied correctly and can quantify what a mishandled epsilon would have cost, rather than discovering only in reconciliation that high-differential periods were quietly under-reported. That visibility is the difference between finding a compressibility-correction error at the meter and inheriting it in the monthly statement.
Because gas loses density as it expands through the pressure drop across the orifice, the actual mass carried by the flowing stream is lower than an incompressible calculation using the upstream density would predict. The expansibility factor multiplies the idealized result down to correct for that, so it sits at or below one. It equals one only when there is no density change, which for practical purposes means a liquid or a vanishingly small pressure drop, and it falls further below one as the differential grows relative to the line pressure.
They describe the same physical effect, the density drop of gas expanding across the orifice, and they behave the same way, starting at one and decreasing as the pressure ratio grows. But they are defined by different standards with their own empirical equations, so a calculation following ISO 5167 must use the ISO 5167 epsilon and one following AGA 3 must use the AGA 3 Y, each paired with its own discharge coefficient and reference conditions. The numbers are close, but the correct one to use depends on which standard the meter is calculated under.
If epsilon is hardcoded or frozen at one operating point rather than computed live, it is only correct at that point and drifts wrong as conditions change. Because the true epsilon falls further below one as the differential pressure rises, a stale value causes the computed flow to be biased during high-differential periods, which are also the high-flow periods carrying the most volume. The result is a systematic under- or over-report that concentrates when the meter is busiest, and it is invisible in the flow reading unless epsilon itself is trended.
This page references the standards, specifications, and official documentation published by the organizations below. Editions, product capabilities, and documentation change over time - confirm current requirements and specifications directly with the source.
Last reviewed: July 27, 2026. Merobix is not affiliated with, endorsed by, or sponsored by these organizations; their names are used only to identify the standards and products discussed.
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