The uncertainty evaluation for the hydrometer calibration at NMISA. Presenter: Bongani Ndlovu Date: 09/10/2018

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1 The uncertainty evaluation for the hydrometer calibration at NMISA Presenter: Bongani Ndlovu Date: 09/10/2018

2 A HYDROMETER Thin graduated hollow tube Weighted at bottom end to make it float upright USED To measure specific gravity, concentration, density of liquids kg/m^3

schoolphysics.co.uk/age11-14/matter/text/hydrometers_/index.

3 HOW IT IS USED Floats in a liquid Liquid density is where Liquid level aligns with the scale e.g., Beer concentration

4 NEED FOR HYDROMETER CALIBRATION Over time, small drifts in scale occur due to Mechanical stress Abrasion Ageing process of glass Calibrate the hydrometer to quantify these small drifts Calibration gives the corrections of the drifts in the scale At NMISA, hydrometers are calibrated on the hydrometer system using Cuckow s method

5 HYDROMETER SYSTEM AT NMISA Consists of 200 g balance with 0,01 mg readability, Tamson TV7000 thermostat, CCD camera, Computer with software, visualization screen

6 SCHEMATIC DIAGRAM Thermostatic bath Inner vessel: Distilled water (reference liquid). 3 T sensors Liquid temperature maintained at 20 C

CUCKOW S METHOD Based on hydrostatic weighing Hydrometer is weighed in air and then in a reference liquid Scale to be calibrated is aligned to the liquid level and the

7 CUCKOW S METHOD Based on hydrostatic weighing Hydrometer is weighed in air and then in a reference liquid Scale to be calibrated is aligned to the liquid level and the reference liquid density is determined at that point Wright JD, Bean VE and Aguilera J, NIST calibration services for hydrometers. NIST Special Publication, 250, 78.

8 Measure: Stem diameter of hydrometer using a Vernier calliper Surface tension of the ref liquid using tensiometer Hydrometer weighed in air: Measure m, air T, RH, P MEASUREMENTS In the reference liquid: Alignment: CCD camera magnified image Measure m, air T, RH, P Liquid T

9 CUCKOW S MODEL CORRECTION: c = ρ x ρ scale where ρ scale is the scale mark to be calibrated S Lorefice et al. Measurement Sc. & tech., 17(10), 2006, 2560

10 UNCERTAINTY BUDGET Depends on several factors including Equipment used Reference liquid Mathematical model (Cuckow s equation) Uncertainty calculations are based on the GUM, 2008

11 Mass in air Mass in liquid HYDROMETER MASS Depend on the reference mass uncertainty and balance properties Ref. mass std. uncertainty (g) Repeatability (g) Resolution (g) Linearity (g) Uncertainty contribution (g) M_a 0, ,0002 0,0001-8E-06 2,24E-04 M_L 0, , , E-05 4,24E-05

12 ADDITIONAL RING WEIGHTS In case of distilled water (ρ 1 g/ml) Hydrometer floats when its density range < 1 g/ml Requires additional ring weight Inner diameter almost equal to the stem diameter Weigh the ring weight in the reference liquid

13 AIR DENSITY Use the CIPM2007 equation Uncertainty depends on the measuring equipment and the equation u T, u RH, u P and u eqn Variable Symbol Unit Value Standard Uncertainty Uncertainty contribution Air temperature T_a C 20,70 0,02-1,13E-03 Air pressure p hpa 875,82 0,06 6,21E-10 Relative humidity rh %rh 38,5 1,3-1,21E-05 Equation 2,28E-08 Air density unc. (g/ml) 1,13E-06 A Picard et al., Metrologia 45 (2008)

14 WATER DENSITY Use the Tanaka formula Density based on SMOW at 1 atm (see level) a 5 = 999,972 kg/m^3 assumed for tap water Apply compressibility correction factor Variable Symbol Units Value Uncert. S_i Uncert. Contribution Water temp T_L C 19,9815 0,06-0, ,238E-05 Air pressure p hpa 875,822 0,06 4,58E-10 2,748E-11 Equation g/ml 4,5E ,5E-07 Water density unc (g/ml) 1,238E-05 M Tanaka et al. Metrologia, 2001, 38,

15 LOCAL GRAVITATIONAL ACCELERATION Gravitational acceleration u g = u of g in the lab Gravitational acceleration gradient (Δg) due to height (h) difference hydrometer in liquid and balance on top u Δg = Δg h

16 OTHER CONTRIBUTORS: IN CUCKOW S MODEL Density of reference mass standard u ρ std = u from density certificate Hydrometer stem diameter u D = u of Vernier calliper Surface tension of the reference liquid u γ = u of the tensiometer Liquid temperature during measurement u T = u of the thermometer Thermal expansion coefficient β (glass) of the hydrometer u β = 10% β

17 ADDITIONAL CONTRIBUTIONS Scale alignment to the liquid level The scale alignment is magnified by CCD camera u align = 1 (hydrometer resolution) 10 Repeatability of the measurement u repeat = ESDM

18 THE UNCERTAINTY BUDGET

19 ρ_x (g/ml) GRAPHICAL REPRESENTATION 1,20E-04 1,00E-04 8,00E-05 6,00E-05 4,00E-05 2,00E-05 0,00E+00 M_a M_L m_r ρ_s γ_x γ_l D g ρ_l ρ_a T_L β S R

20 CONCLUSIONS The uncertainty evaluation for hydrometer calibration at NMISA has been presented The biggest uncertainty contribution came from the surface tension of the reference liquid The uncertainty for the hydrometer calibration can be reduced drastically by using a more suitable (low density, low surface tension) reference liquid (hydrocarbons e.g., tridecane, nonane) than distilled water

21 I THANK YOU

EUROMET Project 702 EUROMET.M.D-K4

EUROMET TC-M Meeting 2007 Thursday, 01 March 2007 EUROMET Project 702 EUROMET.M.D-K4 Comparison of the calibrations of high resolution hydrometers for liquid density determinations Salvatore Lorefice INRIM,