Liquid Flow Meter Calibrations Water Flow Standard

1 Page 1 NIST Special Publication 250-98 LIQUID FLOW METER CALIBRATIONS WITH NIST’s 15 kg/s WATER FLOW STANDARD Jodie G. Pope Aaron N. Johnson B.James Filla Vern E. Bean Michael R. Moldover Joey T. Boyd Christopher J. Crowley Ios... Open at page → 2 Page 2 NIST Special Publication 250-98 LIQUID FLOW METER CALIBRATIONS WITH NIST’s 15 kg/s WATER FLOW STANDARD Jodie G. Pope Aaron N. Johnson B. James Filla Vern E. Bean Michael R. Moldover Joey T. Boyd Christopher J. Crowley Io... Open at page → 3 Page 3 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or... Open at page → 4 Page 4 i This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 LIQUID FLOW METER CALIBRATIONS WITH NIST’s 15 kg/s WATER FLOW STANDARD NIST Special Publication 250-98 Jodie G. Pope, Aaron... Open at page → 5 Page 5 ii This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Contents Abstract ............................................................................................................ Open at page → 6 Page 6 1 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Abstract We describe the 15 kg/s water flow calibration standard operated by the Fluid Metrology Group of the National Insti... Open at page → 7 Page 7 2 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 collection tank of a static gravimetric standard is measured when flow is neither entering nor exiting the tank; hence its w... Open at page → 8 Page 8 3 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 in their laboratory to calibrate other flow meters. The Report of Calibration is the property of the customer. NIST treats t... Open at page → 9 Page 9 4 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 reproducibility [1]. For an example, see the sample calibration report in Appendix A of this document. Variations of the num... Open at page → 10 Page 10 5 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 25 C. [11]) The weigh scale readings are recorded at 0.21 s intervals while the flow accumulates in the collection tank. As... Open at page → 11 Page 11 6 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 4.1 Flow generation, control, and stabilization The 15 kg/s LFS generates and maintains a steady flow and pressure at each s... Open at page → 12 Page 12 7 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 To obtain low-noise dynamic weighings, the water flow between the butterfly valve and the collection tank must be as steady... Open at page → 13 Page 13 8 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 4.3 Test section The test section is a straight, stainless-steel pipe, 3.3 m long with a 5 cm diameter. During flow calibrat... Open at page → 14 Page 14 9 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 r v is the velocity of the fluid at the CS relative to the CS, and ˆn is the outward pointing normal unit vector at the CS.... Open at page → 15 Page 15 10 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 sheet decreases with time because the bottom of the sheet is consumed by the rising water level (L) in the collection tank... Open at page → 16 Page 16 11 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 readings to determine the slope, and hence the mass flow. The linear regression model for the slope is [15]: i i i i 1 1 1... Open at page → 17 Page 17 12 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 0.22 kg/s). The mass of water in the connecting volume will change if either the size of the volume or the water’s density... Open at page → 18 Page 18 13 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 differences between adjacent points in the running averages. We use runm to represent the running- averaged mass flow and u... Open at page → 19 Page 19 14 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 In Eq. (18), m is the mass flow; the subscript STD denotes either the 65 kg/s or the 2.5 L/s LFS; the subscript MUT denotes... Open at page → 20 Page 20 15 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 are discussed in detail in the following sections. As seen in Eqns.(13), (15), and (17) they include the uncertainty contri... Open at page → 21 Page 21 16 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 0.022% and 0.030 %, respectively. The operating requirements of the LFS (minimum collected mass of 44 kg, minimum collectio... Open at page → 22 Page 22 17 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 We used an independent Monte Carlo analysis (not described herein) to confirm that the uncertainty calculations made using... Open at page → 23 Page 23 18 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 2 HOair cal (1 ) Cal Factor W g m      − = , (22) where Cal Factor = 0.99965 ± 2.0×10 -4 and cal m is the calibr... Open at page → 24 Page 24 19 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Dynamic Response and Load Dependence of the Weigh Scale Our procedure for calibrating the weigh scale is valid for static w... Open at page → 25 Page 25 20 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Figure 10 shows multiple sets of data consisting of five repeated calibration points at 13.5 kg/s and 10.5 kg/s and one cal... Open at page → 26 Page 26 21 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 For an acceptable calibration using the 15 kg/s LFS, we require that the calculated uncertainty u(slope) < 0.000045×slope f... Open at page → 27 Page 27 22 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 8.2.b. Buoyancy corrections As shown in Eq. (1), the buoyancy correction to the mass flow LFS m is made by dividing the wei... Open at page → 28 Page 28 23 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 The density change is expressed in terms of the change in in the connecting volume (fi f i T T T = − ), the change in the... Open at page → 29 Page 29 24 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Table 3. Sub-measurements and their uncertainties. The data shown are for a nominal flow of 15 kg/s, however, the uncertain... Open at page → 30 Page 30 25 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 8.2.d. Water density at the MUT Calibrations of volume flow meters such as turbine and positive displacement meters require... Open at page → 31 Page 31 26 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Combined Uncertainty of the Volume Flow at the MUT The volume flow at the MUT is calculated using Eq. (15). The variables i... Open at page → 32 Page 32 27 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 () () ()( ) ()( )( ) MUT LFS 2 22 MUT LFS BED 2 f Q U St k u St k u f u Q s NSS= = + + (37) The uncertainty components for... Open at page → 33 Page 33 28 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 Taking into consideration each component of Eq. (13) and Eq. (15) leads to a combined standard uncertainty of 0.017 % and 0... Open at page → 34 Page 34 29 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 uncertainty can be ascertained from multiple calibrations at NIST. Adding that additional uncertainty to that of the NIST c... Open at page → 35 Page 35 30 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 10.0 References [1] International Vocabulary of Basic and General Terms in Metrology, 2nd ed. International Organization fo... Open at page → 36 Page 36 31 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 98 [18] Aguilera, J., Rainer, E., and Wendt, G. Dynamic-weighing liquid flow calibration system – Realization of a model based... Open at page → 37 Page 37 NIST Test Number: 685-O-0000000000-20-01 Service ID Number: 18020C Calibrated January 27, 2021 by Joey Boyd and Jodie Pope Page 32 of 44 Appendix A: Sample Calibration Report REPORT OF CALIBRATION FOR A CORIOLIS LIQUID F... Open at page → 38 Page 38 REPORT OF CALIBRATION Gas Flow Meter, S/N 12345 Meter, Inc. NIST Test Number: 685-O-0000000000-20-01 Service ID Number: 18020C Calibrated January 27, 2021 by Joey Boyd and Jodie Pope Page 33 of 44 In order to assess the... Open at page → 39 Page 39 REPORT OF CALIBRATION Gas Flow Meter, S/N 12345 Meter, Inc. NIST Test Number: 685-O-0000000000-20-01 Service ID Number: 18020C Calibrated January 27, 2021 by Joey Boyd and Jodie Pope Page 34 of 44 than 0.01% and for the... Open at page → 40 Page 40 REPORT OF CALIBRATION Gas Flow Meter, S/N 12345 Meter, Inc. NIST Test Number: 685-O-0000000000-20-01 Service ID Number: 18020C Calibrated January 27, 2021 by Joey Boyd and Jodie Pope Page 35 of 44 For the Director of the... Open at page → 41 Page 41 36 Appendix B: Formulas for Sensitivity Coefficient Equations Table B1. Formulas for Normalized Sensitivity Coefficients ( ) ( ) i i i i 1 1 1 LFS 2 2 ii 1 air water 1 1 1 N N N i i i NN ii NtW g tW ym N t t  = = = ==... Open at page → 42 Page 42 37 Table B1. Formulas for Normalized Sensitivity Coefficients κ ( ) ref ref ref 1 P TP    −  +  ref P ( ) ref ref ref 1 P TP    −  +  LFS LFS MUT /ymQ == xi ( )/ ( / ) xi i i S y x x y= LFS m Unity MUT ... Open at page → 43 Page 43 38 Appendix C: Nomenclature Variable Description a1, a2 Polynomial coefficients  Volumetric thermal expansion coefficient c Intercept of mass vs. time plot dMUT Inside diameter of meter under test En Normalized degree o... Open at page → 44 Page 44 39 Variable Description s Standard deviation of a sample of N values S Normalized sensitivity coefficient St Strouhal number t Time T Temperature  Period of mass measurements = 209.718 ms u Relative standard uncertainty... 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