# Orifice Flow Measurement Accuracy

## How to Calculate the Zero and Span Errors Caused by the Differences in Temperatures and Pressures Between Calibration and Actual

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Q: My orifice is sized for a range of 0 in. to 100 in. H2O, and we have purchased a dP cell, which the supplier calibrated at ambient conditions and says that it is accurate to 0.05% of URL. With URL being equal to 750 in. H2O, that amounts to an error of 0.375  in. H2O.  I am told that the error contribution of the orifice plate itself is 0.25 % AR (AR = actual reading).

I was asked to determine the measurement error, using the square root of sum of squares method (SRSS) if the flow is 50% (ΔP = 25% = 25 in. H2O), the d/p cell is located where the ambient temperature is 120 ºF, and the operating pressure of the flowing fluid is 1000 psig. I was told that we can neglect the error in the receiving instrument (a computer). How do I calculate the zero and span errors caused by the differences in temperatures and pressures between calibration and actual? What will be my total error at 50% flow if I calculate it with the SRSS method?

Harry Crowney
HCrowney@aol.com

A: The total error of an orifice based measurement is the square root of the sum of the squares of the following errors:

Eo: orifice error;
Eref: reference error (repeatability in Figure 1) stated by the vendor, which reflects only the linearity, repeatability and hysteresis errors of the d/p cell;
Etz, Ets, Epz, Eps, which are the errors caused by the differences between calibration and operating pressures and temperatures on the zero and span of the d/p cell. Usually the "zero error" is the greater if the ratio of upper range limit to full scale (URL/FS) is high;
Era: "rangeability error," which rises as the actual flow drops. For linear meters, it rises linearly (Figure 1). For non-linear, orifice type measurement, it rises exponentionally (ΔP ~ F2), and therefore at 33% flow, the ΔP is 11% FS;
Erc: the error of the receiving instrument.

From Figure 1, one can see that if the supplier publishes only Eref, that is much less than the actual total error, which at 33% full scale flow for a typical installation is about 3%. Therefore, if the flow is expected to drop below 33%, we use multiple ranges (Figure 2).

Béla Lipták
liptakbela@aol.com

A: I would advise two approaches to solve this problem:

1. Send your instruments (transmitter and orifice plate) to CEESI, SWRI or NIST for calibration at cost paid by your company. Ask if they would release certificate of accuracy at 1000 psig, 120 °F first. Ask for the flow determined coefficients.
2. Check the Handbook of Flow Instruments by Dr. Richard Miller. Contact him if necessary. His Flow Consultant software takes thermal expansions of the piping into account, the overall effect of which can influence the accuracy of the instrument by as much as 0.2%.

Gerald Liu, P. Eng.
gerald.liu@shaw.ca

A: There are many issues. First the flow rate, F, is a calculated value related to the differential pressure, dP, created by the orifice. You will need a calibration equation to convert the measured dP to F. In a mathematically ideal world, F is proportional to the square root of dP. However, many features of the orifice design, installation configuration, flow turbulence number (Reynolds Number), fluid compressibility, transducer discrimination errors, etc. often make the square root idealization inappropriate. Often a power law calibration model, such as F=a*dP^b, where b is in the 0.4 to 0.55 range, derived from experimental data, leads to both more accurate and precise results.

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