Water density determination in high-accuracy flowmeter calibration — Measurement uncertainties and practical aspects

In liquid flowmeter calibration, the fluid density is one of the major quantities which impact the uncertainties in the measurement process of calibration. Thus, the in-process density determination in liquid flow standards is revealed as an essential component in the measurement uncertainty analysis.In the case of a volume-reading flowmeter calibrated against a gravimetric reference system, the accurate density value of the actual fluid applied in the calibration facility must be available, by measurement or computation, in order to convert the respective volumetric meter reading into an equivalent mass value. That is necessary, as the reading of the meter under test has to be compared with the reading of the gravimetric reference.Additionally, fluid density related impacts on the measurement uncertainty in a flow standard facility occur in the intermediate pipework which connects the meter under test with the reference device, i.e. the volumetric or gravimetric standard. Due to the difference between the thermal expansion coefficients of the pipework’s material and the enclosed water, a systematic measurement deviation is caused if the temperature of the water and the pipework varies during a calibration run. Practically speaking, such temperature fluctuations always occur due to varying ambient conditions and a more or less imperfect regulation of the water temperature in the flow facility. Thermal expansion implies a change in the fluid density. Thus, this effect, too, has to be taken into account for analyzing the measurement uncertainty of a flow standard facility.This second density related disturbing effect generally occurs in any calibration facility, regardless of whether the meter reading is volume-related or mass-related, and in any combination with a gravimetric or volumetric reference standard.A main issue of this paper is the practical aspect of how to determine the water density in the calibration facility under real conditions, or real conditions referred to, and to derive approximation functions which describe the temperature behavior of water density and which are suitable to be applied for uncertainty analysis purposes.

► Fluid density is an essential source of measurement uncertainty of a water flow standard facility.
► Realistic conditions, like entrapped air in the pipework, must be part of the uncertainty analysis.
► Models of water density functions were derived on the basis of water samples from different origins.
► The approaches utilized are generally applicable to any liquid as test fluid.