Calibration Services for Hydrometers

1 Page 1 NIST Special Publication 250-78r1 NIST Calibration Services for Hydrometers John D. Wright Vern E. Bean Jesus Aguilera This publication is available free of charge from: https://doi.org/10.6028/NIST.SP.250- 78r1 Open at page → 2 Page 2 NIST Special Publication 250-78r1 NIST Calibration Services for Hydrometers John D. Wright Vern E. Bean Jesus Aguilera Sensor Science Division Physical Measurement Laboratory This publication is available free of charge... 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 - 78 r1 Abstract The National Institute of Standards and Technology (NIST) provides calibration services for hydrometers by Cuck... Open at page → 5 Page 5 ii This publication is available free of charge from: https: //doi.org /10.6028/NIST.SP. 250 - 78 r1 Table of Contents Page 1. Description of Service. ........................................................................ Open at page → 6 Page 6 1 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 1. Description of Service. The National Institute of Standards and Technology (NIST) provides calibration services for hy... Open at page → 7 Page 7 2 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Forces due to the liquid- vapor surface tension and the contact angle between the liquid- vapor interface and the hydrome... Open at page → 8 Page 8 3 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Although hydrometers with SI units of g/cm 3 are desirable today, for historical reasons a number of other hydrometer uni... Open at page → 9 Page 9 4 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 The NIST apparatus achieves an expanded (k = 2) uncertainty of 100 parts in 10 6 or less for the calibration results. Cus... Open at page → 10 Page 10 5 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 buoyant force due to the liquid displaced by the volume of the hydrometer below the liquid surface and the buoyant force... Open at page → 11 Page 11 6 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 3 O : balance reading, γT : surface tension of tridecane, Tθ : contact angle of the tridecane on the hydrometer stem, TT... Open at page → 12 Page 12 7 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 ( ) [ ] 23 T T T 0 a2 1( ) OO g V TT αΓ ρβ ρ−+ = + −− (8) where )TT( 0Ta2 −βρ is negligibly small and has been dropped. 5... Open at page → 13 Page 13 8 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 The hydrometer thermal expansion term in Eqns. (9) and (9’) correct for differences in temperature between the calibratio... Open at page → 14 Page 14 9 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 stem intersects the free surface of the tridecane. 2. With the tridecane surface below the scale mark to be calibrated, c... Open at page → 15 Page 15 10 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Figure 3. Surface positioning process The apparatus can be operated in a semi-automatic mode wherein the operator center... Open at page → 16 Page 16 11 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Figure 4. Laser power meter output versus the elevation of the liquid tridecane surface. As the liquid surface traverses... Open at page → 17 Page 17 12 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Initially we used distilled water as the liquid of known density in our apparatus. We had difficulty obtaining reliable... Open at page → 18 Page 18 13 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 1. We measured the density of the tridecane used in our apparatus by applying Arcimedes’ principle to a spherical stainl... Open at page → 19 Page 19 14 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Table 1. Uncertainty analysis for a hydrometer calibrated with the NIST Cuckow’s apparatus. See Table 2 for extra compon... Open at page → 20 Page 20 15 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 11. , 12., and 13. The sinker is needed only when calibrating hydrometers for liquids less dense than tridecane (<0.76 g... Open at page → 21 Page 21 16 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 hydrocarbon liquids, handbook surface tension values are available and uncertainties of 1 mN/m are reasonable. Simple cl... Open at page → 22 Page 22 17 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Table 2. Uncertainty for hydrometer density measurements in water, trichloroethylene, and toluene. Liquid under test Wat... Open at page → 23 Page 23 18 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 9. Validation with Liquids of Known Density The performance of the apparatus was validated with a two step process. Firs... Open at page → 24 Page 24 19 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 10. Comparison to NIST Historical Results for a Reference Hydrometer NIST has a collection of reference hydrometers that... Open at page → 25 Page 25 20 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 11. Summary We constructed and validated an automated standard that calibrates hydrometers by Cuckow’s method. The advan... Open at page → 26 Page 26 21 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 12. Appendix A . Corrections to Hydrometer Readings for Surface Tension Effects A hydrometer floating in a liquid is sub... Open at page → 27 Page 27 22 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 whereDis the hydrometer stem diameter, Vis the volume of the submerged portion of the hydrometer, gis the gravitational... Open at page → 28 Page 28 23 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Hydrometer Calibrated by Hydrostatic Weighing and Used to Measure a Liquid Density Calibration results from hydrostatic... Open at page → 29 Page 29 24 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 where Lγis the surface tension of the liquid being measured, and Rγis the surface tension of the reference liquid used t... Open at page → 30 Page 30 25 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 ( ) 333 γCR cmg9979.0cmg0016.0cmg9995.0 R =−+=∆+= + cρρ Calculate the specific gravity of the oil: ( ) 9989.0 cmg999016.... Open at page → 31 Page 31 26 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 ( )( ) ( ) 3 3 H2Omidmid cm83.48 g/cm999016.0025.1 g50 F60F6060grsp ==== oo ρρ mm V Using Eq. A4, the change in surface... Open at page → 32 Page 32 27 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 hydrometer indicating density correctly when floating in a liquid at temperature 0T, the standard temperature for the in... Open at page → 33 Page 33 28 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 The temperature correction for specific gravity hydrometers is obtained as follows. Assume S to be the reading of a hydr... Open at page → 34 Page 34 29 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 T sp gr 60/60 F 0.7800 0.0064 0.7864 ′=+= + = o Sc . The correction of Eq. B8 can be applied to other hydrometer scales... Open at page → 35 Page 35 30 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 14. Appendix C. Conversion of Liquid Density to Other Hydrometer Scales Hydrometers calibrated in degrees Baumé at 20 °C... Open at page → 36 Page 36 31 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 15. Appendix D. Nomenclature C hydrometer correction, γs cc+= RC hydrometer correction for a reference liquid R LC hydro... Open at page → 37 Page 37 32 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 16. Appendix E. Sample Calibration Report REPORT OF CALIBRATION FOR A HYDROMETER May 18, 2007 Maker: Hydrometer Co. Seri... Open at page → 38 Page 38 33 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 made at NIST, and example hydrometer corrections from Equation (1) assuming a customer surface tension of 25 dynes/cm an... Open at page → 39 Page 39 34 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 Dr. John D. Wright Project Leader, Fluid Metrology Group Process Measurements Division Chemical Science and Technology L... Open at page → 40 Page 40 35 This publication is available free of charge from: https://doi.org /10.6028/NIST.SP. 250 - 78 r1 [12] Adamson A W and Gast A P ( 1997) Physical Chemistry of Surfaces, 6th ed., (New York, John Wiley and Sons). [13] Int... 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