................................................................................................................................................. 1 1.0 Introduction ...................................................................................................................................... 1 2.0 Description of Measurement Services .............................................................................................. 3 3.0 Procedures for Submitting a Flow Meter for Calibration ................................................................. 4 4.0 Description of the Liquid Flow Standard ......................................................................................... 4 4.1 Flow generation, control, and stabilization .................................................................................. 6 4.2 Dynamic weighing system ........................................................................................................... 6 4.3 Test section ................................................................................................................................... 8 5.0 Flow Measurement Principle of Dynamic Weighing ....................................................................... 8 5.1 Mass flow due to storage effects in the connecting volume ....................................................... 11 6.0 Processing the Mass and Time Data to Calculate Flow ................................................................. 12 7.0 Comparison to NIST’s Existing Liquid Flow Standards ................................................................ 13 8.0 Uncertainty ..................................................................................................................................... 14 8.1 Techniques for uncertainty analysis ........................................................................................... 16 8.2 Contributions to the relative standard uncertainties of the mass and volume flow .................... 17 8.2.a. Mass and time measurements ............................................................................................. 17 8.2.b. Buoyancy corrections ......................................................................................................... 22 8.2.c. Mass storage in the connecting volume .............................................................................. 22 ...................................................................................................................................................... 24 8.2.d. Water density at the MUT .................................................................................................. 25 8.3 Combined uncertainty of the LFS mass and volume flow ......................................................... 25 8.4 Combined and expanded uncertainty of the calibration factor ................................................... 26 8.5 Uncertainty considerations for a customer meter under test ...................................................... 28 9.0 Summary ........................................................................................................................................ 29 10.0 References .................................................................................................................................... 30 Appendix A: Sample Calibration Report ............................................................................................. 32 Appendix B: Formulas for Sensitivity Coefficient Equations .............................................................. 36 Appendix C: Nomenclature .................................................................................................................. 38

The National Institute of Standards and Technology (NIST) provides calibration services for hydrometers by Cuckow's method, i.e. by weighing the hydrometer while it is immersed to specified scale markings in a liquid of known density (tridecane).Normally a calibration is done at three points, at approximately 10 %, 50 %, and 90 % of the scale.The calibration report includes a simple equation for each calibration point that gives the user a correction to the hydrometer reading that accounts for the surface tension of the liquid in which the hydrometer is used.The calibration results have an expanded uncertainty (with coverage factor of 2) of 100 parts in 10 6 or less of the liquid density.The apparatus was validated by comparisons using liquids of known density: water, toluene, tridecane, and trichloroethylene.Results from these comparisons agreed within 40 parts in 10 6 or less.

We describe an automated apparatus for calibrating hydrometers by hydrostatic weighing (Cuckow's method) in tridecane, a liquid of known, stable density, and with a relatively low surface tension and contact angle against glass. The apparatus uses a laser light sheet and a laser power meter to position the tridecane surface at the hydrometer scale mark to be calibrated with an uncertainty of 0.08 mm. The calibration results have an expanded uncertainty (with a coverage factor of 2) of 100 parts in 106 or less of the liquid density. We validated the apparatus by comparisons using water, toluene, tridecane and trichloroethylene, and found agreement within 40 parts in 106 or less. The new calibration method is consistent with earlier, manual calibrations performed by NIST. When customers use calibrated hydrometers, they may encounter uncertainties of 370 parts in 106 or larger due to surface tension, contact angle and temperature effects.

Problem: Since their establishment in the late 1960's and early 1970's, the standards of the NIST Fluid Flow Group (FFG) have only seen incre- mental upgrades. During the same period, a number of generations of flow sensors have been introduced into the market. Current leading technologies for flow meters have performance levels that challenge the uncertainty of U.S. standards. This places the American metrology community at a competitive disadvantage because they cannot claim uncertain- ties lower that those attained by our National stan- dards while remaining traceable to NIST. Further- more, National Metrology Institutes in other indus- trialized countries have recognized the importance of flow metrology standards to economic growth and have made large capital investments to upgrade their National standards. Examples of such facilities are the new state-of-the-art water calibration facili- ties in CENAM-Mexico and PTB-Germany, and the refurbished facility at NRLM-Japan; the natural gas calibration facilities of TransCanada Calibrations- Canada and Pigsar-Germany; and the new gas flow calibration facilities of IMGC-Italy and NRLM-