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An Uncertainty Analysis for a PositiveDisplacement Liquid Flow Calibrator Usingthe Water Draw TechniqueWesley B. EnglandU.S. Army Primary Standards LaboratoryThis paper is an uncertainty analysis performed by the Liquid Flow Lab of the Army Primary Standards Laboratory (APSL)for the calibration of positive displacement piston prover using a volumetric water draw. The water draw calibration isconducted to establish a precise relationship between translator pulses and the volume of liquid displaced by the draw andis known as the K-Factor (given in pulses/unit volume). For the APSL the term “Water Draw” is a misnomer, because theAPSL uses hydrocarbons that are already in the flow calibrator at the time of the draw calibration.IntroductionThe purpose of a water draw calibration is to providetraceability either volumetrically or gravimetrically toa Positive Displacement Piston Liquid Flow Calibrator.A simple schematic of a Positive Displacement LiquidFlow Calibrator is shown below in Figure 1.The positive displacement liquid flow calibratorconsists of a piston cylinder flow element and measuresflow rates through a Device Under Test (DUT) asillustrated in the following manner. In Figure 1 abovethe piston starts at position 1 (x 1) at time (t 1) on the xaxis and being set into motion by air pressure moves ina positive direction along the x axis to position 2 (x 2) intime (t 2). The displacement of the piston (x 2– x 1) dividedby the time duration it took for the piston to move fromposition 1 to position 2 (t 2– t 1) gives us the rate in [UnitLength/Unit Time] the piston has traveled in the positivex direction and is given by the following expression asRate =____​( x -x 2 1t 2-t 1)​ = ​ ___ ΔxΔt ​ = __ ​ dxdt ​ . (1)Since the piston and cylinder are circular, the areaof the piston cylinder arrangement is given by A = πr 2and if we know the radius of the circle we can calculateits area. If we multiply the constant area by the rate inFigure 1. A Simple Schematic of a Positive Displacement Liquid Flow Calibrator.Jan • Feb • Mar 201331Cal Lab: The International Journal of Metrology