Pressure gauge calibration: procedure, points and uncertainty

A pressure gauge is calibrated by comparing it against a reference at a series of pressures spanning its range, with the comparison made in both directions. The rest is detail, but the detail is where the errors are: which pressure you mean, what the fluid column between the two instruments is doing, and whether the gauge was tapped before it was read.

Which pressure are you measuring?

Three measurands share the word and they are not interchangeable. Gauge pressure is measured relative to whatever the ambient atmosphere happens to be at the time. Absolute pressure is measured from a vacuum. Differential pressure is the difference between two ports, neither of which need be atmospheric. A gauge reading 1 bar gauge and an instrument reading 1 bar absolute are describing conditions that differ by roughly a whole atmosphere.

The practical consequence: a certificate must state the mode. If it does not, you cannot use the result, because you do not know what the numbers are referenced to. This is one of the most common gaps in pressure certificates from general-purpose laboratories.

The procedure in outline

• Mount the gauge in its normal orientation. A mechanical gauge calibrated lying down and used upright has had its element loaded differently.
• Record ambient temperature; pressure instruments are temperature-sensitive and the certificate should say what the temperature was.
• Exercise the gauge: take it to full scale and back two or three times before recording anything, so the mechanism is working over its normal travel.
• Rising series: approach each point from below and hold until stable, never overshooting and coming back.
• Falling series: from full scale, approach each point from above, with the same discipline.
• At least five points across the span, including zero and full scale, is the usual minimum; more if the gauge is used over a narrow band you care about.
• Repeat the cycle if repeatability is to be quantified rather than assumed.

Approaching a point from the wrong direction is the single easiest way to produce a result that looks better than the instrument is. The whole reason for two series is to see the difference between them.

Hysteresis, and why one direction is not enough

A Bourdon tube, a diaphragm or a bellows does not return along the path it took. The reading at 5 bar on the way up and at 5 bar on the way down can differ by more than every other error combined, and on a well-used mechanical gauge hysteresis of half a scale division is unremarkable. A calibration that only ever went up reports the instrument at its most flattering and tells you nothing about how it behaves in service, where pressure falls as often as it rises.

The head correction people forget

If the reference and the gauge under test sit at different heights and the medium between them is liquid, the column of fluid adds pressure to the lower instrument. For water the effect is about 98 pascals per centimetre of height; for oil it depends on the density of that oil. Over a half-metre bench height difference in a water-filled rig that is roughly 5 kPa — which will be larger than the uncertainty you were claiming.

With a gas medium the same correction exists and is usually negligible, but "usually" is doing real work in that sentence at low pressures and large height differences. The honest approach is to record the height difference and the medium, apply the correction, and say in the certificate that you did.

Building the uncertainty

The contributions that normally matter, roughly in order of size for a mechanical gauge:

• Resolution of the gauge — for an analogue dial, how finely you can honestly interpolate between divisions, which is rarely better than a fifth.
• Hysteresis, from the difference between the rising and falling series.
• Repeatability, from repeated cycles.
• Uncertainty of the reference, from its own certificate, at the point being used.
• Drift of the reference since its last calibration.
• Head correction, if the height difference was estimated rather than measured.
• Temperature effects, where the calibration temperature differs from the temperature of use.

For a digital gauge the ordering changes: resolution is usually small, and the reference uncertainty and the gauge's own repeatability dominate. Either way the arithmetic is the ordinary one — combine in quadrature, expand for the coverage you are reporting at.

Reading the certificate you get back

• Does it state gauge, absolute or differential?
• Does it show both rising and falling values, or only one column?
• Is the uncertainty given at each point, or one figure for the whole range? A single figure across a wide span is often the worst case quoted everywhere.
• Is there a conformity statement, and if so, against which tolerance and on what decision rule?
• Was the gauge adjusted? If so, are there as-found and as-left values, or only as-left?
• What medium and what orientation?

A certificate showing only as-left values on an adjusted gauge has thrown away the evidence you need. As-found is what tells you whether anything measured with that gauge since the last calibration is in doubt.