CIPM Air Density 1981_91Password to unlock:metrologyDo not delete these cellsAir Density CalculationThey are used to calculate air density.Barometric Pressure:727.55mm Hg96998.6891447371PaTemperature:21.40C294.55KRelative Humidity:47.00%47.00%Calculated Air Density:1.142182795mg/cm30.001142g/cm3NOTE: When copying these cells into a spreadsheet, they must be pasted into exactlythe same cells on a new worksheet (i.e., the block from A3 to G7).Cell references in the equations are "absolute" and fixed to the reference cells in each equation.Once the cells are pasted, the entire block may be dragged/dropped.

&APage &P of &N

Air Density - ValidationAir Density CalculationsPassword to unlock:metrologyData Entry and Data Set ComparisonsEquations and VariablesActive Fortran ProgramSOP 2, Option AReference EquationsPressure:760.000000mm Hgra1.2000583135((0.4646*(H4-(0.003796*H6*L5)))/(273.15+H5))Temperature:20Ces17.53568856731314600000*EXP(-5315.56/(H5+273.15))Relative humidity:42%SOP 2, Option B (preferred for all precision work)Pressure (converted):101325Para1.2000655177(L10*(L11/(L12*L13*L14))*(1-0.378*L15)), Giacomo version of base equation (1982)Temperature (converted):293.15KMa2.90E-020.0289635 (28.96386 in 1981 version)p101325PaZ9.996203E-011-((L11/L14)*(L24+L25*H5+L26*H5^2+(L27+L28*H5)*L15+(L29+L30*H5)*L15^2))+(L11^2/L14^2)*(L31+L32*L15^2)CIPM 81/91 Paper Data Sets, Table 2Reference ConversionsR8.314518.314510E+00PatRHmm HgPaT293.15KData Set 11000002050750.061682704168100000xv9.73505E-03(L16/100)*L17*(L18/L19)Data Set 21100002010825.067850974584110000h42%Data Set 31000001590750.061682704168100000f1.0040256051.00062+(0.0000000314*L19)+(0.00000056*H5^2)Data Set 4600002550450.03700962250160000rsv2.33916E+031*EXP(L20*L14^2+L21*L14+L22+L23/L14)Uncertainty in Air Density Equation:0.0012Pa = mm Hg * 133.322368421053p101325PaA1.24E-051.2378847E-05Comparison of Calculation ResultsB-1.91E-02-1.9121316E-02Set 1C33.9371104733.93711047SOP 2, A1.1834636D-6.34E+03-6.3431645E+03SOP 2, B1.1834717a01.58E-061.58123E-06air91co24.exe1.1834720a1-2.93E-08-2.9331E-08a21.10E-101.1043E-10CIPM Paper1.1834720b05.71E-065.707E-06b1-2.05E-08-2.051E-08c01.99E-041.9898E-04Set 2c1-2.38E-06-2.376E-06SOP 2, A1.3065573d1.83E-111.83E-11SOP 2, B1.3065817e-7.65E-09-7.650E-09air91co24.exe1.3065820References:CIPM Paper1.3065820Equation for the Determination of the Density of Moist Air (1981)Metrologia 1982, 18, 33-40P. GiacomoSet 3Equation for the Determination of the Density of Moist Air (1981/91)SOP 2, A1.2023136Metrologia, 1992, 29, 67-70SOP 2, B1.2024079R. S. Davisair91co24.exe1.2024080Handbook 145, SOP 2CIPM Paper1.2024080R. S. DavisAir91co24.exeCreated in Fortran by Zeina J. JabbourSet 4Based on 4 % CO2 concentration.SOP 2, A0.6942524SOP 2, B0.6941618air91co24.xlsair91co24.exe0.6941617Created by Georgia L. Harris, Feb 2003CIMP Paper0.6941620NIST SP 811; conversion factors for Pa and mm Hg

&APage &P of &N

Kragten - Air Density UncCIMP 1981/91 Formula, R. S. DavisAir Density CalculationsKragten SpreadsheetABCDP (mm Hg)T (C)RH (%)Equation12346Pressure:760.000000mm HgPressure:760.500000mm HgPressure:760.000000mm HgPressure:760.000000mm Hg1Value760.000020.000042.00000.0000Temperature:20.0000CTemperature:20.0000CTemperature:20.1000CTemperature:20.0000C2Uncertainty0.50.1000010.000000.0012Relative humidity:42.0000%Relative humidity:42.0000%Relative humidity:42.0000%Relative humidity:52.0000%P (mm Hg)3760.000000760.5000760.0000760.0000760.0000T (C)420.00000020.000020.100020.000020.0000133.3223684211RH (%)542.00000042.000042.000052.000042.0000ra1.2000655177ra1.2008582178ra1.1996277588ra1.1990185085Equation60.0000000.00000.00000.00000.0012Ma2.90E-02Ma2.90E-02Ma2.90E-02Ma2.90E-02Corr (x)71.2000661.2008581.1996281.1990191.201266p101325p101391.661184211p101325p101325u(y,xi)80.000793-0.000438-0.0010470.001200Z0.9996202685Z0.9996200384Z0.999621099Z0.999613335u(y)2, u(y,xi)293.356E-066.28E-071.92E-071E-061.44E-06R8.31451R8.31451R8.31451R8.31451u(c)100.00183243.27%23.90%57.15%65.50%T293.15T293.15T293.25T293.15k11219%6%33%43%xv9.73505E-03xv9.72867E-03xv9.79554E-03xv1.20529E-02k*u120.003664100%h42h42h42h52100*ku/c(x)130.153< relative unc. (%) at k=1f1.004025605f1.0040276982f1.0040278506f1.004025605rsv2.33916E+03rsv2.33916E+03rsv2.35369E+03rsv2.33916E+03Green Cells for P, T, RH, and their uncertainties may be changed.p101325p101391.661184211p101325p101325A1.24E-05A1.24E-05A1.24E-05A1.24E-05B-1.91E-02B-1.91E-02B-1.91E-02B-1.91E-02C33.93711047C33.93711047C33.93711047C33.93711047D-6.34E+03D-6.34E+03D-6.34E+03D-6.34E+03a01.58E-06a01.58E-06a01.58E-06a01.58E-06a1-2.93E-08a1-2.93E-08a1-2.93E-08a1-2.93E-08a21.10E-10a21.10E-10a21.10E-10a21.10E-10b05.71E-06b05.71E-06b05.71E-06b05.71E-06b1-2.05E-08b1-2.05E-08b1-2.05E-08b1-2.05E-08c01.99E-04c01.99E-04c01.99E-04c01.99E-04c1-2.38E-06c1-2.38E-06c1-2.38E-06c1-2.38E-06d1.83E-11d1.83E-11d1.83E-11d1.83E-11e-7.65E-09e-7.65E-09e-7.65E-09e-7.65E-09Password to unlock:metrology

&APage &P of &N

Kragten - Air Density Unc

VariablePercent of UncUncertainties for Air Density EquationCIPM 1981/91 Equation

MABC & MABC UncertaintySOP 2, MABCKragten SpreadsheetABCDEEntered ValuesUncertaintiesCalculated ValuesMassrarnrxrsMass100g0.025Delta rho-0.05123467ra1.15mg/cm30.0012Vx12.75510204081Value100.00001.15001.20007.84008.0000rn1.2mg/cm30Vs12.52Uncertainty0.0250.001200.000000.050000.00800rx7.84g/cm30.05MABC-0.012755102Mass3100.000000100.0250100.0000100.0000100.0000100.0000rs8g/cm30.008ra41.1500001.15001.15121.15001.15001.1500rn51.2000001.20001.20001.20001.20001.200000rx67.8400007.84007.84007.84007.89007.8400R 111 Uncertainty for the buoyancy correction.rs8.0000008.00008.00008.00008.0000008.0080Corr (x)7-0.012755-0.012758-0.012449-0.012755-0.008714-0.013379u(y,xi)8-0.0000030.0003060.0000000.004042-0.000624u(y)2, u(y,xi)291.682E-051.02E-119.37E-080E+001.63E-053.90E-07u(c)100.0041010.08%7.46%0.00%98.55%15.23%ubc0.0003061222k1120%1%0%97%2%k*u120.008202100%100*ku/c(x)13-32.151< relative unc. (%) at k=1Green Cells for Mass, air density, normal air density, density of the standard and unknown and their uncertaintiesmay be changed.m011111rho a0.911.11.21.3rho n1.21.21.21.21.2rho x77.57.99688.4rho s88888-0.0053571429-0.0016666667-0.00000625310-0.0005952381Password to unlock:metrology

&APage &P of &N

MABC & MABC Uncertainty

VariablePercent of UncUncertainties for MABCUnc of the correction, not Unc of MABC

Georgia L Harris:

MBD00BB5162.unknown

MBD02044C46.unknown

MBD010E634A/air91CO24.exe