Analysis of Flow Meters Calibration

Calibration data of flow meters are often reported using the so called calibration coefficient, i.e. the ratio between the reference flow rate (or equivalent quantity, e.g. airspeed, accumulated volume etc.) and the corresponding quantity as indicated by the instrument to be calibrated. The main reasons for this choice are twofold: - First of all, this approach is very practical for the end user of the instrument, who can get the corrected flow rate by simple multiplication of the readout times the coefficient; - Second, this representation allows to highlight the non-linearities of the instrument, which usually show up in the lower end of the range and might be hidden by a direct representation. On the other hand, this approach makes the uncertainty evaluation of the resulting data more complex, because of the correlation between the regression data. In this paper, we will perform an analysis according to such traditional approach and also according to an alternate “direct” approach, i.e., considering the reference flow rate as the dependent variable, instead of the calibration coefficient. In both cases the regression will be performed by a specific software for calibration curves (CCC software, developed at INRIM in the framework of the EMRP NEW04 Project). Fig. 1 shows, as a case example, the scatter plot and the relevant regression curve for the two data representations. A procedural approach for correctly performing regression and uncertainty evaluation will be derived for both methods, and the results obtained will be compared. Specific attention will be devoted to the non-linear response region of the instrument range, since this part of the range is the more delicate and often the one where the instrument is used for a significant fraction of its operational life.