National measurement standard of liquid density unit: structure, metrological characteristics, and operation principles

The article presents the structure, composition, operation principle, and metrological characteristics of the national primary measurement standard of liquid density unit. This measurement standard realizes the liquid density unit by reference procedure and is the basis for comparison and metrological traceability for other measurement standards of liquid density unit, that made it possible to give it the national primary standard status. Based on accuracy characteristics analysis of primary measurement standards from other countries (CMC-lines from the KCDB of the International Bureau of Weights and Measures based on key and supplementary comparisons), it is possible to prove its high metrological status and initiate international comparisons for establishing its metrological equivalence to the analogical measurement standards from other countries. Measurement standard operation algorithms (in weighting and comparing mode) and uncertainty sources contributing to the uncertainty budget of liquid density measurement, which make it possible to submit measurement results according to established international requirements, are analyzed in the publication.

• Mass comparator Mettler Toledo AX 1005 with the following characteristics: -maximum load -1109 g; -electrical weighing range -from 0 to 109 g; -standard deviation of mass comparator -0,0148 mg obtained as a result of three series comparisons of two weights with the same nominal weight for ten ABBA weighting cycles under the same conditions with an interval of no more than seven days between series calculated using the formula:

The basis for the development of the primary measurement standard of liquid density unit in Ukraine, its metrological characteristics, composition, and structure
Measurement standard base is the scientific and technical basis for ensuring measurement traceability in the country and contributes to the development of the scientific and production sector of the economy, international trade, and consumer protection [1] .
Liquid density unit is among the physical quantity units, realization and dissemination of which is extremely important in many spheres of economy, particularly in energy, oil and gas (for example, in hydrocarbon processing), medicine, and during production processes, ensuring proper conditions for testing products.The demand for metrological traceability for working standards and working measuring equipment in the range from 500 to 2000 kg/m 3 currently exists.• Set of Е2 class weights with nominal value from 1 g to 500 g and expanded uncertainty from 0,01 to 0,25 mg.
• PC and software for measurement standard.
It should be noted that the reference silicon measure (Fig. 1) is a basis for ensuring measuring traceability of liquid density measurement results [4]

Structure and operation of measurement standard
Analysing the structure of measurement standard of liquid density that unit realizes primary reference measurement method grounded on hydrostatic weighting principle using reference silicon measure that has determined mass and volume values and determines its status of primary measurement standard [5] .
By this method, liquid density is determined where M -the mass of reference measure, kg; g m -the acceleration of gravity, m/s 2 ; V -the volume of reference measure, m 3 ; ρ -liquid density, kg/m 3 ; w -the result of reference mass weighting in liquid, kg; w V -weights volume, m 3 ; e -air density, kg/m 3 .
Replacing weights volume w V in equation ( 1) with w E , where E is measure's material density (usually for corrections in mass estimation E = 8000 kg/m 3 is taken) for finding the expression for liquid density estimation from formula (1): (2) Air density ( e ) is calculated by the formula CIPM-2007 «Revised formula for the density of moist air» [6] (further -CIPM-2007).
The measurement standard of the liquid density unit structure scheme that realizes the above method of liquid density unit dissemination is presented in Fig. 3. -reference silicon measure; -reference glass measure for density; -mass comparator; -air characteristics control system; -liquid temperature control stabilizing system; -liquid level control system; -weighting system; -system for automating the process of measurements and processing results.

Liquid density unit realization algorithm and measurement result uncertainty evaluation
To determine liquid density, one should provide a repeated weighting of reference measure for density (silicon measure, glass measure) in liquid using one of the algorithms (weighting or comparing).Double distilled water, water-ethanol solutions, rectified ethanol, etc., can be used as liquid.

Liquid density unit realization algorithm using national primary measurement standard in weighting mode
Reference measure for density is weighted using hydrostatic weighting installation in weighting mode not less than 10 times.During each weighting, air pressure, air temperature, and relative humidity characteristics are recorded by the device for measuring air characteristics, and air density is estimated according to CIPM-2007.
Studied liquid density in weighting mode is calculated by the formula: Formula 3 takes into account that the liquid temperature may differ from the set temperature since it is more convenient to weight measure in liquid which temperature is the same or almost the same as the facility.This makes it possible to ensure precision requirements.If the current liquid temperature deviates from 20 °С then the reference measure for density volume V T at a temperature T is calcu- lated by a formula: where V 20 -the reference measure for density volume defined at a temperature 20 °С; β -temperature volume expansion factor of ma- terial from which the density measure was produced K -1 (value for silicon measure 0,0000077 K -1 in the temperature range from 15 °С to 20 °С).

Liquid density unit realization algorithm using national primary measurement standard in comparing mode
The following operations are provided in comparing mode: -reference measure for density (silicon sphere) is weighted in liquid; -set of replacing measures is weighted; -reference measure for density and set of replacing measures are weighted repeatedly; -during each weighting, air pressure, air temperature, and relative humidity characteristics are recorded by the device for measuring air characteristics, and air density is estimated according to CIPM-2007; -weighting cycle is repeated not less than 10 times.
Liquid density ρ , kg/m 3 , calculation in each cycle in comparing mode is provided by a formula: where M -reference measure for density mass, kg (g); V -reference measure for density volume, m 3 (cm 3 ); G -summary conventional mass of weights set taken from calibration certificate, kg (g); g -comparator readings during weights set weighting, kg (g); w -comparator readings during reference mea- sure for density weighting in liquid, kg (g); e -air density at a moment of measurement kg/m 3 (g/cm 3 ); E -conventional density of weights material (is assumed to be 8000 kg/m 3 ), kg/m 3 (g/cm 3 ); β -temperature volume expansion factor of liquid, К -1 ; ∆T -the difference between the set tempera- ture for liquid density measurement and actual liquid temperature according to indication of reference thermometer (T ), °С.
The average of obtained values is selected as a final result, in both modes weighting and comparing: where n -number of measurements; ρ -obtained value of liquid density in each measurement kg/m 3 (g/cm 3 ).

Uncertainty evaluation of liquid density unit realization obtained using national primary measurement standard
Type B uncertainty (due to instrumental components) evaluation is conducted depending on the selected measurement mode.
For weighting mode standard Type B uncertainty of liquid density measurement result is calculated by a formula: where where weight 1 g -0,005 mg weight 2 g -0,006 mg weight 5 g -0,008 mg weight 10 g -0,01 mg weight 20 g -0,0125 mg weight 50 g -0,015 mg weight 100 g -0,025 g weight 200 g -0,05 mg weight 500 g -0,125 mg weight 1000 g -0,25 mg Determined by the calibration certificate of the mass comparator From the source of information about a particular liquid or is assumed 1 10 due to the absence of information

Table. 3. Analytical expressions for impact factors of equation (9) and standard uncertainties sources for components
Combined standard and expanded uncertainties are calculated based on the uncertainty budget for particular circumstances of measurement using mathematical expressions from Tables 2 and 3.
The combined standard uncertainty of the liquid density measurement result is calculated by the formula kg/m 3 (g/cm 3 ): The expanded uncertainty of the liquid density measurement result is calculated by the formula kg/m 3 (g/cm 3 ): coverage factor k = 2 (level of confidence P = 0 95 , ).
A system for measurement automation and measurement results processing (Fig. 5) was developed to simplify measurement using the national primary standard unit of liquid density and to process measurement results.

Conclusions
The national primary measurement standard of liquid density unit realizes disseminating density unit by reference procedure using hydrostatic weighting.
Values range in which the density unit is realized, maintained, and disseminated is from 650 to 2000 kg/m 3 .Herewith, the combined standard uncertainty is 1,75 ⋅ 10 -3 kg/m 3 and measurement stan- dard instability is not more than 2 10 3 ⋅ − kg/m 3 .Ob- tained characteristics of primary measurement standard correspond to analogical characteristics of primary measurement standards from other countries (CMC-lines from KCDB of International Bureau of Weights and Measures), it is possible to prove its high metrological compatibility and initiate scientific international comparisons for establishing its metrological equivalence to the analogical measurement standards from other countries.

For
this reason, according to the Order of the Ministry of Economic Development, Trade and Agriculture of Ukraine dated 25.02.2019№ 317, «On plans approval for scientific, research, and development works by the Ministry of Economic Development, Trade of Ukraine in metrology and standardization spheres in 2019» [2] plan for scientific, research, and development works by the Ministry of Economic Development, Trade of Ukraine in metrology and standardization spheres in 2019 was approved and SE «Ukrmetrteststandart» was tasked with developing a primary standard of liquid density unit.The primary measurement standard of liquid density unit was developed as a result.It is assigned for realizing and maintaining the density unit -kilogram per cubic meter (gram per cubic centimeter) and disseminating its unit to the secondary standards and measurement standards and measuring equipment in the range of density values from 650 kg/m 3 to 2000 kg/m 3 that are used for measurements in food, chemical, oil refining industry, agriculture, medicine, etc. aiming to assure uniformity of measurement in the sphere of liquid density measurements within the country.in the country, and its metrological characteristics were determined in the calibration process of the measure in the National Metrology Institute of Germany PTB (certificate № PTB-11316/18).Set of reference glass measures for density that are part of the measurement standard and are used to disseminate the liquid density unit to the secondary standard of liquid density unit, or determination of liquid density, that is, reference materials characterization.Reference glass measures should be used for both primary and secondary measurement standards.

Fig. 1 .
Fig. 1.Reference silicon measure ensures liquid density unit realization and is included in the National primary measurement standard of liquid density unit Mass comparator, set of weights, thermostat, platinum resistance thermometer АМ1950 complete with thermometric bridge ТР-3200, ДВТ-161 pressure, humidity, and temperature sensors were calibrated for determining actual metrological characteristics.Foundations on which measurement standard is placed have decoupled design, that is, the foundation of the column for the mass comparator is poured separate from the foundation of the hydrostatic weighting installation lifting mechanism.Support columns and hydrostatic weighting installation for measurement standard structure were developed, and their installation with the following adjustment was carried out by employees of Shtalygin&Co («Шатлигін і К0») and SE «Ukrmetrteststandart».The measurement standard general view is presented in Fig. 2.

•
The instrument for measuring air parameters ДВТ-161 includes pressure, humidity, and temperature sensors with the following metrological characteristics: -atmospheric pressure measurement range from 600 to 800 mm Hg; -air temperature measurement range from 15 to 25 °С; -relative air humidity measurement range from 30 to 70 %; -expanded uncertainty of absolute pressure measurement result is 3 mm Hg; -expanded uncertainty of air temperature measurement result is 0,5 °С; -expanded uncertainty of relative air humidity measurement result is 3 %.

Fig. 2 .
Fig. 2. Measurement standard of liquid density unit general view: а) measurement standard schematic view; b) measurement standard of liquid density unit photo from the SE «Ukrmetrteststandart» laboratory by the weighting of the measure (reference silicon sphere) loaded in this liquid.The equilibrium equation for weight during measure in liquid weighting, taking into account Archimedes' force influencing the measure in liquid (pushing force) and weights of the mass comparator that are in the air, has the following form:

Fig. 3 .
Fig. 3. Measurement standard of liquid density unit structure scheme Uncertainty of liquid density measurement consists of two components: uncertainty due to variability of a measured value is evaluated by Type A, and instrumental uncertainty component due to measurement equation and instrumental component values are evaluated by Type B. Regardless of selected experiment mode, standard Type A uncertainty of liquid density u A ρ ( ) measurement result is estimated by a formula: uncertainties of values that are inclu- ded in equation (9);c M ( ), c V ( ), c G ( ), c g ( ), c w ( ), c e ( ), c E ( ), c β ( ),c T ∆ ( ) -impact factors that are included in equa- tion (9) and are estimated as corresponding partial derivatives from density for that characte-

Fig. 5 .
Fig. 5. System for measurement automation and measurement results processing

Table 1 .
The conclusion from Table1proves the national − kg/m 3 20 °СTable. 1. Measurement standards of liquid density unit operated on the hydrostatic weighting principle passed international comparisons and obtained CMC-lines © 2021 Measurements infrastructure national Bureau of Weights and Measures are presented in