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The comparison method

How in-situ flow meter calibration works

The most practical way to prove a flow meter in a working plant is to put a calibrated reference next to it and compare the two under the same conditions. This page explains that method step by step — what the master meter is, what the meter under test is, what gets recorded, and why the result is worth having.

Isometric diagram of a calibration setup. Fluid flows from left to right through a pipe. It passes first through the master meter, the traceable reference instrument, then along a straight run of ten pipe diameters into the meter under test, and leaves through a further straight run of five pipe diameters. Both straight runs belong to the meter under test and are provided where its type requires them. A data acquisition unit below reads both meters at the same time and calculates the percentage deviation between them.

Flow REFERENCE UNDER TEST 10 × D (where required) 5 × D (where required)

Swipe the diagram sideways to see the whole run.

Simultaneous data acquisition

REFERENCE50.0 m³/h
UNDER TEST49.6 m³/h
DEVIATION−0.8 %
Master meterTraceable calibration
Meter under testYour installed instrument

10 × D straight run before the meter under test (where required)5 × D straight run after the meter under test (where required)

  1. 1 One flow, two instrumentsBoth meters are in series, so exactly the same fluid at the same rate passes through each. Any difference between the readings belongs to the instruments, not to the process.
  2. 2 The master meter is the known quantityIt holds its own accredited calibration certificate and an unbroken traceability chain to national standards. It is the yardstick, and it is the reason the result means anything.
  3. 3 Straight runs protect the measurementBends, valves and pumps distort the velocity profile, and a distorted profile is read differently by different meters. Undisturbed pipe either side of the meter under test — where its type calls for it — keeps the comparison honest.
  4. 4 The deviation is the deliverableReadings are logged simultaneously for at least 180 seconds per run, at three to five flow rates with repeats. The percentage difference at each rate, plus the repeatability across runs, is what goes on the certificate.

The five ways a flow meter can be calibrated

Calibration means comparing an instrument against a known standard and documenting the difference. For flow there is more than one way to establish that standard, and each one buys accuracy at a different price in time, access and disruption. These are the five recognised methods, and where each of them genuinely fits.

  • Gravimetric method

    The fluid that has passed through the meter is collected in a vessel standing on a scale, and its mass is weighed. Mass and elapsed time give the true flow rate, which is then compared with what the meter reported.

    Suited to
    Low flow rates and the tightest accuracy requirements; it is the primary standard many national metrology institutes are built on.
    Limitation
    Slow, laboratory-bound and impractical at large sizes or for a meter that has to keep running in a live process.
  • Volumetric method

    The meter is compared against a calibrated volume standard — a proving vessel or pipe prover — so the volume that actually passed is known independently of the meter.

    Suited to
    Positive-displacement meters and any duty where volume, not mass, is the traded quantity.
    Limitation
    Generally a higher uncertainty than gravimetric weighing, particularly at low flow.
  • Master meter method

    A high-precision reference meter with its own documented, traceable calibration is placed in the same line, and the meter under test is compared against it. The reference itself indicates the reference flow rate, traceable to the SI units.

    Suited to
    Large meters, plant conditions and any case where a laboratory rig cannot be brought to the measurement — this is the method behind our mobile rig.
    Limitation
    The result can never be better than the reference: its own uncertainty and stability are part of every figure reported.
  • Comparison method

    The general form of the above: the meter under test is compared against another meter of known, higher accuracy, and the difference between the two readings is the deviation. In practice this and the master meter method are run as one procedure — comparison calibration.

    Suited to
    A wide range of meter types and installations, provided a reference of adequate accuracy and range exists for the duty.
    Limitation
    The whole calibration rests on the accuracy of the reference chosen, which is why selecting it for the line is part of the procedure rather than an afterthought.
  • In-situ calibration

    The meter is calibrated where it is installed, in its own process, without being removed. It is verified under the conditions it actually works in — the fluid, the temperature, the pipe run and the flow profile it really sees.

    Suited to
    Meters that cannot be taken out of service, are difficult to access, or whose installation is itself the suspected source of error.
    Limitation
    A higher stated uncertainty than a controlled laboratory rig, because the conditions are the plant's rather than the laboratory's.

Why we calibrate by master-meter comparison

  • The flow configuration is far simpler than a gravimetric standard needs, because the reference meter itself indicates the reference flow rate, traceable to the SI units — no weighing vessel, no diverter.
  • Maintenance effort and cost are lower than for a gravimetric standard, which is what makes a mobile rig realistic in the first place.
  • It takes less time and effort per meter, so several points on the same line can be calibrated in one visit.
  • It applies to a wide range of liquid flow meters, so one procedure covers most of what a plant actually has installed.
  • It is compatible with the GUM, the guide to the expression of uncertainty in measurement (ISO/IEC Guide 98-3:2008), and it is the working standard chosen by many accredited flow laboratories worldwide.

And the part that is usually left out

The guidelines for the master meter method are not as fully established as those for gravimetric standards, because the uncertainty of relative deviations is less well understood than the system uncertainty of a weighing rig. It is not enough to combine the reference's uncertainty with the meter under test's: the long-term stability of the reference, the uncertainty of the associated instruments and — following the WGFF guideline — a cross-correlation term between reference and meter under test all belong in the budget. That last term exists because the two flow rates are not independent: the continuity equation ties them together along the same pipeline. Anyone who quotes you a comparison uncertainty without those terms has quoted you a smaller number than the truth.

The comparison method, step by step

  1. 1 Read what the meter under test actually outputsFirst we establish the signal we are going to judge: pulses or an analogue current, and the resolution of that output. A deviation smaller than the resolution of the signal cannot be resolved at all, so this determines what the calibration can honestly claim before anything is installed.
  2. 2 Select the reference for the lineThe reference meter is chosen for the maximum flow rate of the line, so the whole working range of the meter under test sits inside the reference's own calibrated range. A reference used outside its range is the largest error source in the exercise, not the smallest.
  3. 3 Fit the reference in series, with the right inlet and outlet sectionsThe traceable reference goes into the same line as the meter under test, usually into a spool piece prepared for the purpose, so both instruments see identical flow. The inlet and outlet pipe sections are made up as the meter under test requires — ten pipe diameters of undisturbed pipe before it and five after, where its type calls for that. Where the line cannot be broken, a clamp-on ultrasonic reference is used instead, and where the installation cannot provide the straight runs we record the actual installation as part of the finding.
  4. 4 Zero the instruments and match the acquisition chainZero calibration is performed on both the reference and the meter under test, and the flow computer input is set to the meter under test's analogue output range — 4–20 mA or 0–20 mA — so that what we log is the number the plant sees, not a rescaled version of it.
  5. 5 Fill the line, check for leaks, purge the airThe pump is started and the whole rig is pre-filled, checked for leaks, and air bubbles are removed along the pipeline. Entrained air is measured as volume by both instruments and by neither of them equally, so a bubble is a deviation that belongs to nobody.
  6. 6 Confirm every signal before any data is keptWorking the flow control valves, we confirm that pulses, currents, temperature and pressure all respond as they should. Data collection starts only once the whole chain has been seen to behave — a dead channel discovered afterwards costs the whole visit.
  7. 7 Establish steady state at each set pointFlow is set with the control valve and then left to settle. The delay caused by the change in the valve's open-area ratio is allowed for deliberately, so a run never begins on a flow that is still moving towards its set point.
  8. 8 Record both meters simultaneously, at least 180 seconds per runThe reference and the meter under test are logged at the same instant for a minimum of 180 seconds per run — longer on request — with the temperature and pressure of the working fluid recorded alongside them, because the fluid conditions are part of the result.
  9. 9 Three to five flow points, each repeated three to five timesThe points are chosen by the client or by the calibration engineer, spread across the actual working range. Every point is repeated three to five times: the repeats are what confirm linearity across the range and give a repeatability figure, instead of one lucky reading per rate.
  10. 10 Calculate the deviation and compare it with the specificationThe error of the totalizer, or of the flow rate, is calculated at each point as a relative deviation in per cent of reading, together with the spread across the repeat runs. Those figures are then compared with the manufacturer's specification or with your own limits. This is the as-found result, and it stands whether or not anything is adjusted afterwards.
  11. 11 Adjust only if you ask for it, then run it againWhere the meter allows a correction and you accept the error, the new calibration factor is the old calibration factor multiplied by the adjust factor, and the weighted mean error is recomputed. The measurement runs are then repeated in full. If the corrected error falls inside the manufacturer's specification or your own boundaries, the verification is signed off as a pass.
  12. 12 Issue the certificate — as-found and as-leftThe final document consists of two verification sheets: the as-found certificate before any adjustment, and the as-left certificate after it. Between them they state the points tested, the deviation and repeatability at each one, the reference instrument and its traceability chain, the expanded uncertainty with its coverage factor, the fluid conditions, any installation findings and the recommended next interval.

The vocabulary on the certificate

Master meter — reference meter (REF)
A high-accuracy flow meter whose own calibration is documented and traceable to national standards. It is not part of the plant; it is brought in, used as the yardstick, and taken away. Its accuracy has to be substantially better than the tolerance you are trying to prove, and its own uncertainty and long-term stability are carried into every figure we report.
Meter under test — MUT, also DUT (device under test)
The instrument installed in your plant, the one whose readings you rely on. Method documents and uncertainty budgets normally call it the DUT; on a flow certificate you will see both abbreviations for the same instrument. The purpose of the exercise is to find out how far it has moved from correct, under real operating conditions rather than in a laboratory.
Relative deviation (E)
The quantity a comparison calibration actually reports: how far the meter under test sits from the reference, as a fraction of the reference reading, expressed as a percentage. It is a relative figure by design — that is what makes it comparable between visits, between meters and between flow rates.
Repeatability
The spread of repeated runs at the same flow rate — in statistical terms the standard deviation of the mean of the runs. It answers a different question from the deviation: a meter with a constant offset is correctable, whereas a meter that gives a different answer each time under identical flow needs service or replacement, not a new calibration factor.
Traceability
An unbroken chain of calibrations linking the reference meter back to a national or international standard, each step documented and each with a stated uncertainty. Without it, a calibration certificate is just an opinion on paper.
Measurement uncertainty
Not the error, and not a tolerance: it is the parameter associated with a measurement result that characterises the dispersion of the values that could reasonably be attributed to the measured quantity. Every measurement has one, it is always stated as an absolute value with no plus or minus sign of its own, and a certificate that omits it is incomplete — a deviation of 0.4 % means nothing if the uncertainty of the comparison is 1 %.
Calibration factor and weighted mean error (WME)
Where a meter can be corrected, the new calibration factor is the old one multiplied by an adjust factor derived from the measured deviations, and the weighted mean error across the tested range is recomputed with it. The runs are then repeated, so the corrected meter is proven rather than assumed.
As-found / as-left
The readings before and after any adjustment, issued as two separate verification sheets. As-found tells you how wrong the plant has been since the last calibration — which is the figure that matters for anything already invoiced or reported. As-left tells you where it starts from now.

How the number is calculated, and what its uncertainty is made of

A comparison calibration produces one headline figure per flow point, and that figure is only worth as much as the budget behind it. This is how it is computed and which contributions go into it — the same terms our ISO/IEC 17025 method document puts in front of the accreditation body.

The reported quantity

E = (q_DUT / q_REF) − 1

The relative deviation E compares the mass passing the meter under test with the mass passing the reference. Since mass flow is volume flow times density, and both instruments sit on the same line carrying the same fluid, the densities cancel as long as the temperature is under control — which is why the comparison can be treated as a ratio of volume flow rates. For water we calculate density from the measured temperature using a formula valid between 0 °C and 40 °C: holding the temperature within 20 ± 0.2 °C moves the density only from 998.16 to 998.24 kg/m³, less than ±0.04 kg/m³, and that is small enough to neglect. This is also why temperature and pressure are logged on every run rather than assumed.

Standard uncertainty, u(x)
The uncertainty of a single contribution, expressed as a standard deviation. Divided by the best estimate of the quantity it becomes the relative standard uncertainty, which is what lets contributions in different units be compared and combined.
Type A and Type B evaluation
Type A is calculated statistically, from the spread of the measurements we actually took — which is why the repeats at each flow point exist. Type B is everything established by other means: a reference certificate, an instrument specification, engineering judgement about a known effect.
Combined standard uncertainty, u_c(y)
The individual contributions, each weighted by its sensitivity coefficient — how much the result moves when that input moves — and combined as the root sum of squares. The sensitivity coefficients are what stop an irrelevant input from inflating the budget and a critical one from disappearing into it.
Expanded uncertainty, U, and coverage factor k
The combined uncertainty multiplied by a coverage factor, typically between 2 and 3, to give an interval expected to contain a large fraction of the plausible values. We report at k = 2, corresponding to approximately 95 % confidence, and we state the coverage factor rather than leaving you to guess which one was used — a figure quoted at k = 1 looks half as large for no better reason.
Correlation between reference and meter under test
The two flow rates are not independent quantities: the continuity equation ties them together along the same pipeline. Treating them as independent understates the uncertainty, so a cross-correlation term between reference and meter under test belongs in the budget, as the WGFF guideline sets out.
Long-term stability and associated instruments
The reference does not stay identical between its own calibrations, and the flow computer, temperature and pressure instruments each contribute. Those terms are part of the uncertainty of the comparison, not a footnote to it.
Calibration and Measurement Capability (CMC)
The uncertainty a laboratory can declare for a given measurement. Following the Working Group for Fluid Flow, it is the root sum of squares of a Type B base uncertainty of the reference standard, propagated as the GUM describes, and a Type A repeatability obtained from repeated calibrations of the best existing device, evaluated at set points across the range of the capability rather than at one convenient rate.
Reported uncertainty on your certificate
What appears on the certificate combines that capability with the repeatability actually observed on your meter, at 95 % confidence with k = 2. Two meters calibrated on the same rig can therefore carry different reported uncertainties — the unstable one honestly carries the larger figure.

The documents this method is built on

  • GUM — Guide to the expression of uncertainty in measurement (ISO/IEC Guide 98-3:2008)
  • VIM — International vocabulary of basic and general terms in metrology
  • ISO 5168:2005 — Measurement of fluid flow: procedures for the evaluation of uncertainties
  • WGFF Guidelines for CMC Uncertainty and Calibration Report Uncertainty
  • ISO/IEC 17025 — general requirements for the competence of testing and calibration laboratories

Calibration procedures follow ISO/IEC 17025 methodology; ESYD accreditation is in progress.

Why calibration is needed at all

Instruments do not announce that they have stopped being accurate. They keep producing plausible numbers, and every decision downstream inherits the error.

Drift is gradual and silent

Sensors age, electronics shift and mechanical parts wear. Nothing alarms, because from the instrument's point of view nothing is wrong — it reports its new reality with full confidence.

Coating, wear and corrosion

Deposits on an electrode, a worn turbine bearing, an eroded orifice plate or a scaled liner all change the relationship between flow and signal that the original calibration assumed.

The process moved, the calibration did not

A new fluid, a different temperature or viscosity, a modified pipe run, a replaced pump. The instrument is still calibrated — for conditions that no longer exist.

Mass balance stops closing

When inputs and outputs disagree, the argument is about which meter is wrong. A calibration answers that question with evidence instead of seniority.

Custody transfer and billing

Where a meter decides what is invoiced, its error is money moving in one direction. A documented error percentage is what makes an invoice defensible.

Compliance and audit evidence

Quality systems, environmental permits and customer audits all ask the same question: how do you know this measurement is right? A traceable certificate is the answer.

Safety functions

Where a measurement feeds an alarm or interlock, an undetected error is a protective function that will not act when it is needed.

Maintenance planning

A history of as-found values turns instrument maintenance from reactive replacement into a planned, evidence-based interval.

What a 1 % flow error is actually worth

Take a line carrying 50 m³/h of a medium valued at €0.40 per m³, running 6,000 hours a year. That is 300,000 m³ and €120,000 of throughput annually. A 1 % measurement error — well inside what an uncalibrated meter can drift by without anyone noticing — misstates €1,200 every year on that single point. On a custody-transfer or billing meter the same percentage applies directly to what is invoiced, and it accumulates silently in whichever direction the drift happens to go.

Substitute your own rate, unit value and running hours: the arithmetic is deliberately simple, because the point is the order of magnitude. On most plants a single calibration costs a fraction of one year of undetected error on one important meter.

Traceability and uncertainty, in plain language

  • Our reference instruments are calibrated by accredited laboratories, and those certificates are the foundation of every result we issue.
  • Each certificate names the specific reference instrument used, so any measurement can be tied back to the standard behind it.
  • Every stated deviation is accompanied by the uncertainty of the comparison, with its coverage factor and confidence level, because an error figure without an uncertainty cannot be judged.
  • The tested points and conditions are recorded — flow rates, number of runs, fluid temperature and pressure — so a later calibration can be compared against a like-for-like baseline rather than a different set of conditions.
  • Our calibration procedures are built to ISO/IEC 17025 requirements, and our ESYD accreditation is in progress.

When in-situ comparison is not the right answer

This method is powerful but it is not universal. Being clear about that up front saves everyone a wasted visit, and a number nobody should trust is worse than no number at all.

  • Very large diameter lines where no reference meter of adequate range is available.
  • Multiphase flow — gas entrained in liquid, or slurries — where neither instrument measures a well-defined quantity.
  • Flow rates below the usable range of the reference, where the reference itself is the largest source of error.
  • Lines that cannot be isolated or fitted with a spool piece, and whose geometry or material rules out a clamp-on reference.
  • Tolerances tight enough that only a laboratory flow rig can deliver the required uncertainty.
  • Installations so disturbed — a meter directly on a bend or pump discharge — that the honest finding is to correct the installation first.

Common questions

Keep your instrumentation performing at its best

Speak with SEMAC's service team to discuss your maintenance needs and plan your verification & calibration service.