Calibration Services for Liquid Volume

1 Page 1 NIST Calibration Services for Liquid Volume NIST Special Publication 250-72 Vern E. Bean, Pedro I. Espina, John. D. Wright, John F. Houser, Sherry D. Sheckels, and Aaron N. Johnson March 24, 2006 Fluid Metrology Group Pr... Open at page → 2 Page 2 Liquid Volume Calibration Service NIST SP 250-72 Table of Contents Page 1. Description of Service.................................................................................................................1 2. Desig... Open at page → 3 Page 3 Liquid Volume Calibration Service NIST SP 250-72 1. Description of Service. The National Institute of Standards and Technology (NIST) provides calibration services for metal volume provers for volumes up to 2000 gal (760... Open at page → 4 Page 4 Liquid Volume Calibration Service NIST SP 250-72 methods: gravimetric methods and volume transfer methods. In the gravimetric method, the volume of distilled water required to fill a volume prover up to its full referenc... Open at page → 5 Page 5 Liquid Volume Calibration Service NIST SP 250-72 Figure 2. Neck scale volume prover, top emptying style. Measurements of contained volume and delivered volume are both vital to commerce. Contained volume is the volume of... Open at page → 6 Page 6 Liquid Volume Calibration Service NIST SP 250-72 Figure 3. Neck scale volume prover, bottom drain style. 3. Description of NIST Facilities 3.1 Gravimetric Facility The mass of distilled water required to fill a volume pr... Open at page → 7 Page 7 Liquid Volume Calibration Service NIST SP 250-72 than 380 L (100 gal). Typically, the 60 kg weigh scale is used for volume provers of 38 L (10 gal) or smaller, while the 600 kg weigh scale is used for volume provers from... Open at page → 8 Page 8 Liquid Volume Calibration Service NIST SP 250-72 drained by pouring, with the volume prover held at an angle of approximately 70° with respect to horizontal, including 10 seconds after the cessation of the main flow. Gen... Open at page → 9 Page 9 Liquid Volume Calibration Service NIST SP 250-72 5. Measure the temperature of the water in the volume prover, record the readings, and then remove the temperature sensors. 6. Measure and record the room air temperature,... Open at page → 10 Page 10 Liquid Volume Calibration Service NIST SP 250-72 () () h T mm TV = airw ef wcontain − − − ρρ (3) where: h is the deviation of the location of the meniscus from zero (in m 3 ) with the appropriate algebraic sign applied.... Open at page → 11 Page 11 Liquid Volume Calibration Service NIST SP 250-72 scale and so . 0≡h Omit steps related to measuring the height of the water in the neck and set equal to 0 in equations 3 and 4. h 4.1.3 Gravimetric Transfer Method: Pre-we... Open at page → 12 Page 12 Liquid Volume Calibration Service NIST SP 250-72 13. Read and record the deviation of the location of the meniscus from zero on the neck scale in volume units. 14. Measure the temperature of the water in the volume prove... Open at page → 13 Page 13 Liquid Volume Calibration Service NIST SP 250-72 6. Measure and record the room air temperature, atmospheric pressure, and relative humidity. 7. If possible, measure the temperature of the water in the volume prover unde... Open at page → 14 Page 14 Liquid Volume Calibration Service NIST SP 250-72 height. 2. Level the volume prover under test at an appropriate location with respect to the elevated platform. 3. Provide appropriate plumbing between the drain of the wo... Open at page → 15 Page 15 Liquid Volume Calibration Service NIST SP 250-72 sign applied, t,wT is the temperature of the water in the volume prover under test. Equation 8 will yield contained volume at T if the inside walls of the prover under tes... Open at page → 16 Page 16 Liquid Volume Calibration Service NIST SP 250-72 4.2.2 Volume Transfer Method: Slicker Plate Volume Prover to Neck Scale Volume Prover When a neck scale volume prover is calibrated using a slicker plate working standard,... Open at page → 17 Page 17 Liquid Volume Calibration Service NIST SP 250-72 )( )] - ( + )[1 + ()( = )( t,w ref,ss,wssss,w t,wdeliver T TThVT TV ρ βρ (11) 4.3 Neck Scale Calibrations Neck scales can be calibrated by various methods, including: 1. V... Open at page → 18 Page 18 Liquid Volume Calibration Service NIST SP 250-72 and 5), the neck scale calibrations will apply to contained volume rather than delivered volume. 5. Viscosity Corrections Volume calibration is done at ambient laboratory... Open at page → 19 Page 19 Liquid Volume Calibration Service NIST SP 250-72 () 3122986 10178.91004326.1104994.51076263.1 TTTT −−−− ×−×+×−×=ν (16) Equation 16 was obtained by fitting a polynomial to the ratio of dynamic viscosity to density for wat... Open at page → 20 Page 20 Liquid Volume Calibration Service NIST SP 250-72 the most common calibration performed, there are 9 values for V, 5 at approximately zero on neck scale and 4 distributed over the range of the neck scale. One can calculat... Open at page → 21 Page 21 Liquid Volume Calibration Service NIST SP 250-72 () ()()() 2 1 2 2 V ji n 1i 1n 1ij ji ji 2 2 n 1i i i V , 21 =         + ∂ ∂ ∂ ∂ +         ∂ ∂ ∑∑∑ = − +== V xxrxuxu x V x V V xu x V V kU σ (19) where: re... Open at page → 22 Page 22 Liquid Volume Calibration Service NIST SP 250-72 temperature dependant terms would be unwieldy, its first order approximation is used in this uncertainty analysis: () ( )[ ] 0ww0w 1 TTT −−= βρρ (20) where 0ρ is the densi... Open at page → 23 Page 23 Liquid Volume Calibration Service NIST SP 250-72 ()νu is the uncertainty due to viscosity effects on delivered volume (Type B), and is the variance of replicated determinations of prover volume (Type A). 2 V σ The expres... Open at page → 24 Page 24 Liquid Volume Calibration Service NIST SP 250-72 Tables 1 through 4 show data reduction spreadsheets and uncertainty calculations for four volume provers: 42 gal, 21 gal, 5 gal (all with neck scales), and a 5 gal slicker... Open at page → 25 Page 25 Liquid Volume Calibration Service NIST SP 250-72 Table 1. Sample spreadsheet with uncertainty analysis for the gravimetric determination of of a 42 gal (160 L) graduated neck scale volume prover. See text for key. ( refd... Open at page → 26 Page 26 Liquid Volume Calibration Service NIST SP 250-72 Table 2. Sample spreadsheet with uncertainty analysis for the gravimetric determination of of a 21 gal (80 L) graduated neck scale volume prover. ( refdeliverTV ) Page 24... Open at page → 27 Page 27 Liquid Volume Calibration Service NIST SP 250-72 Table 3. Sample spreadsheet with uncertainty analysis for the gravimetric determination of of a 5 gal (19 L) graduated neck scale volume prover. ( refdeliverTV ) Page 25 M... Open at page → 28 Page 28 Liquid Volume Calibration Service NIST SP 250-72 Table 4. Sample spreadsheet with uncertainty analysis for the gravimetric determination of of a 5 gal (19 L) slicker plate volume prover. ( refdeliverTV ) Page 26 March 24... Open at page → 29 Page 29 Liquid Volume Calibration Service NIST SP 250-72 7.2 Uncertainty of the Volume Transfer Method In this section, we will analyze the uncertainty of the volume transfer method using the example of the calibration of a 450... Open at page → 30 Page 30 Liquid Volume Calibration Service NIST SP 250-72 Explanatory notes for Tables 5 and 6 are given below. A) Volume prover identification, size, volume per smallest scale division. B) Temperature sensor calibration coeffici... Open at page → 31 Page 31 Liquid Volume Calibration Service NIST SP 250-72 Table 5. Sample of the worksheet that totalizes the mass for the volume transfer method, 4 × 100 gal + 1 × 50 gal ≈ 450 gal. See text for key. Page 29 March 24, 2006 Open at page → 32 Page 32 Liquid Volume Calibration Service NIST SP 250-72 Table 6. Summary of the five repeated measurements, averages, and sample uncertainty analysis for the volume transfer method. See text for key. Page 30 March 24, 2006 Open at page → 33 Page 33 Liquid Volume Calibration Service NIST SP 250-72 8. References Bird, R. B., Stewart, W. E., and Lightfoot E. N., Transport Phenomena , Wiley, New York, 1960, pp. 69. Chemical Rubber Publishing Company, Handbook of Chemis... Open at page → 34 Page 34 Page 32 Appendix A. Calibration of Weigh Scales The traceability of liquid volume measurements to the national standards of mass is through a 65 kg set of weights calibrated by the NIST Acoustics, Mass, and Vibrations Gr... Open at page → 35 Page 35 Page 33 5. Add a 0.2 kg sensitivity weight, m, and record the reading as O, s 3         −+= s air s23 1 ρ ρ mOO where sρ is the density of the metal from which the sensitivity weight is made, 6. Remove , reset th... Open at page → 36 Page 36 Page 34 Calibration of the 60 kg and 600 kg Weigh Scales The 60 kg weigh scale is calibrated by placing weights from the 65 kg set on the platform in 5 kg increments for the up-loading cycle. The down-loading increments... Open at page → 37 Page 37 Page 35 Appendix B. Derivation of Equations for Gravimetric Method for Neck Scale Provers In the gravimetric procedures for neck scale volume provers listed in Section 4.1.1, the weigh scales readings for the dry volume... Open at page → 38 Page 38 Page 36 where residualw,M is the water remaining in the measure after the valve is closed at the end of the specified drain time. For the measure filled with water up to the zero reference mark, () () ()        ... Open at page → 39 Page 39 Page 37 Appendix C. Derivation of Equation for the Volume Transfer Method The transfer method of volume calibration is accomplished by emptying a known volume of water from a working standard measure into the measure to... Open at page → 40 Page 40 is the temperature of the water in the measure under test, and tw,T )( tw,Tρ is the density of the water in the working standard. Since mass is conserved in the transfer process, equations 1C and 2C are solved for and th... Open at page → 41 Page 41 Appendix D. Sample Calibration Report REPORT OF CALIBRATION FOR A ONE HUNDRED (100) GALLON VESSEL (Graduated Neck Type) April 28, 2005 NIST Seal Number: 1234 Material: Stainless Steel Manufacturer: Test Measure Co. Gaith... Open at page → 42 Page 42 REPORT OF CALIBRATION NIST Seal No.: 1234 Test Measure Co. Purchase Order No. ABC123 Table 1. Contained and delivered volumes for the tested vessel for a scale reading [2] of zero. gal at 60 °F in 3 at 60 °F Volume Conta... Open at page → 43 Page 43 REPORT OF CALIBRATION NIST Seal No.: 1234 Test Measure Co. Purchase Order No. ABC123 04/22/02 10/13/98 04/26/05 23088 23089 23090 23091 23092 23093 23094 23095 23096 23097 23098 1998 2000 2002 2003 2005 2007 Year Deliver... Open at page → 44 Page 44 REPORT OF CALIBRATION NIST Seal No.: 1234 Test Measure Co. Purchase Order No. ABC123 NIST Test Number: 836/123456-05-01 Page 4 of 4 Calibration Date: April 26, 2005 by Sherry Sheckels and John Wright Open at page →