key: cord-1034543-rqs5vtqg
authors: Hernández-Vásquez, José Daniel; Pedraza-Yepes, Cristian Antonio; Rodriguez-Salas, Andrés David; Bolívar-Solana, Jorge Luis; Gonzalez-Camacho, Darío Andres
title: Evaluation of the metrological reliability of a graduated cylinder from experimental data from an in-situ calibration
date: 2020-08-06
journal: Data Brief
DOI: 10.1016/j.dib.2020.106133
sha: 3a64fdbd9fc9e55d081e0f116bc06f67b03d7019
doc_id: 1034543
cord_uid: rqs5vtqg

This work presents the data experimentally collected in a chemical laboratory for the calibration of a graduated cylinder. There are several factors that can influence the volume measurement using this type of instrument and, consequently, its metrological reliability, for example: the internal geometry, the environmental conditions (ambient temperature, atmospheric pressure and relative humidity), the acceleration of gravity, the density of the air, among others. For the data collection it was necessary to use a glass liquid thermometer (Range: 0 to 10 °C), a digital thermohygrometer (Range: 0 to 100 °C and 0 to 99 %RH) and a digital barometer (Range: 0 to 9999 mbar). Additionally, an analytical scale (Range: 0 to 220 g) was used for mass measurement. From the measurements obtained, it was possible to determine the in-situ air density and the buoyancy factor that influences the mass measurement. The data, rigorously obtained, present a potential use to determine the metrological reliability of a graduated cylinder for laboratory use and, additionally, contribute to perform a metrological validation of alternative methods for the calibration of graduated cylinder.

The ambient temperature must not exceed 25 o C. The analytical balance must be located on a flat surface, balanced and free from drafts, as well as from vibrations. In addition, it must wait 25 minutes for its use. At this point an electronic balance of its parts is expected. Distilled water should be used at room temperature. Additionally, the standard masses must be thermally equilibrated with the ambient temperature. For this they should be used after 30 minutes.

Once the first calibration of the digital scale was completed, the graduated cylinder was calibrated. Pure water was used for this activity and the total volume of the graduated cylinder was achieved by introducing small volumes (approximately 0.5 ml in 0.5 ml). At each experimental point the water temperature was measured with the help of the liquid glass thermometer. Additionally, atmospheric pressure and ambient temperature were measured (manufacturer: Forecast; Range: 0 a 9999 mbar; Resolution: 1 mbar). The objective of increasing the volume of the graduated cylinder in small volumes was to reduce the impact of non-homogeneity related to the internal diameter. Once the calibration of the balance was finished, the calibration of the graduated cylinder was carried out without discounting its initial mass. The graduated cylinder was calibrated, 91 experimental points were obtained, to total the maximum volumetric capacity of 50 ml.

Universidad del Atlántico, Barranquilla, Colombia.

With the article

 Documented data is particularly important because it allows an in-depth assessment of the contribution of error and uncertainty of the tare function to the mass measurement process.

 The published data is very important for professionals in the physical, chemical and engineering areas. With this data and the applied methodology, they can assess the metrological reliability of not only scales, but also electronic devices for measuring temperature, pressure and other digital instruments.

 From the published data it is possible to apply other statistical methods associated with the uncertainty analysis (example: Monte Carlo method) and to evaluate the potentiality of these methods applied to electronic devices used in a laboratory.

 In the medium term, the results of similar research, using published data, are expected to contribute to improving the reliability of measurements for drug manufacturing. Furthermore, in this era where high metrological reliability of measurement equipment is required to investigate a vaccine against covid-19.

 As an added value, the published data was obtained by applying high scientific rigor, using measurement standards traceable to the International System of Units. This becomes an unquestionable reliability of the results and discussions that can be obtained by applying analytical methods. Table 2 presents the experimental data. Applying the uncertainty expansion theory [1] [2] [3] [4] and using the certificate of calibration [5] was possible to calculate the uncertainty associated to the standard mass. Moreover, Table 2 shows, in highlight, the indicated mass by the analytical scale, the apparent mass and its uncertainty. In relation to the measurement uncertainty, it can be seen that the values associated with the standard mass are in the order of micrograms. This confirms that the metrological hierarchy of the mass standards used to obtain the data. In relation to the measurement uncertainty associated with temperature, it can be seen that the obtained value of 0.029 o C is at least three times less than the resolution of the instrument used. This confirms the high accuracy associated with the temperature measurement process. Finally, the calculated value for air density (1.14 kg/m 3 ) is in line with the average values found in the literature (approximately 1.2 kg/m 3 ) and its measurement uncertainty is much less than the tabulated values. and published in the literature, approximately equal to 5% of the measured value (i.e.: 0.06 kg/m 3 ). Table 2 shows that the uncertainty obtained for the air density varies between 0.00069 kg/m 3 to 0.00070 kg/m 3 . Unquestionably, this confirms the scientific rigor with which the experiments have been carried out and, consequently, the obtaining of the data. The environmental temperature and the atmospheric pressure were measured using calibrated instruments. The certificate of calibration reports the uncertainty in 0.029 o C for the thermometer and 0.60 mbar/abs for the barometer [5] . This data are showed in the ascending and descending load situations. Once the dataset in the previous table were obtained, the method of ordinary least squares was applied, whose foundations are detailed in other works [6] [7] [8] [9] . This method allowed establishing a relationship between the mass indicated by the analytical scale (horizontal axis) and the apparent mass calculated (vertical axis). In this way, the uncertainty of the adjustment of four different polynomials (grade 1, 2, 3 and 4) was evaluated. It was obtained that the first degree polynomial is the one that best represents the physical nature of the problem, once its uncertainty of adjustment (i.e.:, the uncertainty that adds to the calibration process the fact of making an adjustment polynomial) turned out to be the least of all. The uncertainty value of the adjustment is equal to 0.0028 g. Figure 1 shows the calibration curve obtained, as well as the adjustment equation. In this figure we can see the coefficients of the first-degree fit equation (y = ax + b) where a corresponds to the slope (a = 1.0052) and b corresponds to the intercept with the vertical axis (b = 74.0069 ). The determination coefficient R2 represents the agreement between the mathematical model and the analyzed physical phenomenon. The obtained value (R 2 = 1.0000) is a clear example of the excellent relationship between the mathematical model and the physical model. The expanded uncertainty associated to mass measurement is calculated. Table 3 shows the dataset for the ascending and descending load situations: mass indicated by the analytical scale and mass adjusted by the polynomial. In addition, The uncertainty analysis, for each experimental point, is shown. The combined uncertainty is calculated from the adjusted uncertainty , standard mass uncertainty and the uncertainty associated to the resolution of the analytical scale -this value can be obtained by dividing half the resolution of the instrument by the square root of three ( √ ), to associate it with a rectangular probability distribution. The coverture factor is calculated form t-student distribution and a number of degrees of freedom , where m is a number of experimental data and n is the number of constant coefficients of the adjustment polynomial. For the specific case of the calibration of the analytical balance applying the Tare Function, the number of experimental points is equal to 204 and 2 are the constants of the first degree polynomial. Then, the calculated degree of freedom number is equal to 202. Table 3 presented above confirms the value of the expanded uncertainty obtained (U = 0.0055 g) for a confidence level of 95.45%. This data confirms, despite being a low value compared to the resolution of the instrument, it can be improved by not using the tare function. That is, without affecting the electronic system of the balance. This is detailed in the next sections.

Similarly, to the procedure described in the before section, the Table 4 presents the experimental data obtained when the Tare Function was not applied in the calibration analytical scale process. This table shows 204 experimental data and the standard mass value which was increasing each 0.5 g. The environmental temperature and the atmospheric pressure were measured for each experimental point. For the ascending and descending load, Table 5 presents the experimental data for this new situation (without applying Tare Function), in terms of: indicated mass by the analytical scale, apparent mass calculated, uncertainty of apparent mass, environmental temperature, atmospheric pressure, air density, as well as its uncertainty. Once the dataset showed in Table 5 , the method of ordinary least squares was applied. This method allowed establishing a relationship between the mass indicated by the analytical scale (horizontal axis) and the apparent mass calculated (vertical axis). In this case, the polynomial that better adjusted the physical nature of the problem was a fourth degree polynomial and its uncertainty of adjustment is 0.00063 g. Figure 2 shows the calibration curve obtained, as well as the adjustment equation. For this new situation, the mathematical model that best fits the physical phenomenon corresponds to a fourth degree polynomial whose constant coefficients are observed in Figure 2 . The determination coefficient confirms the excellent agreement between the mathematical and physical model. Table 6 shows the dataset associated to expanded uncertainty. The corresponding coverage factor is equal to 1.97 (for a confidence level equal to 95.0%). However, in this case, the expanded uncertainty associated to mass measurement is less than the before situation. The estimated value was 0.0012 g. According to the data presented in Table 6 above, it is observed that the expanded uncertainty (U = 0.0012 g) is approximately five times less than that presented in Table 3 (U = 0.0055 g), which confirms that there is an undesirable measurement error that contributes to a dismissal of the metrological reliability of a digital scale when using the tare function.

In the course of the experiments, carried out in a chemical laboratory [5] , an analytical balance (manufacturer: Ohaus) with a resolution of 0.0001 g and a measurement range from 0 to 210 g was used for mass measurement. The graduated cylinder used (manufacturer: Brand) has a volumetric capacity declared in 50 ml and a scale division equal to 1 ml. For the measurement of liquid temperature, a liquid in glass thermometer with a measuring range of 0 to 100 o C and a scale division equal to 0.1 o C was used. For the measurement of the environmental conditions a digital thermohygrometer (manufacturer: HTC) was used with a resolution equal to 0.1 o C and a measuring range of 0.0 to 99.9 o C in temperature.

In addition, to offering a resolution of 1% RH and a range maximum up to 80% RH for the case of relative humidity (RH) measurement. Additionally, a barometer with a resolution of 1 mbar was used to measure the atmospheric pressure. Figure 3 illustrates an experimental assembly scheme.

The experiment was started by calibrating the analytical balance according to the OIML R-76-1 guidelines. An E1 class weight set [5, 10] was used. Two situations were evaluated in the calibration of the graduated cylinder: (i) placing the graduated cylinder in the load cell and applying the tare function. Subsequently, the graduated cylinder is removed from the load cell and the calibration process begins; (ii) initiating the calibration process without discounting the mass of the graduated cylinder. In both cases, once the scale was switched on, there was a 90-minute wait for the stabilization of the electronic system, according to the recommendations of the manufacturer. In addition, in both situations evaluated, 204 experimental points were obtained (102 in for Ascending Load and 102 for Descending Load.). Once the first calibration of the balance was completed (Applying the Tare Function), the graduated cylinder was calibrated. Pure water was used for this activity [11] and the total volume of the graduated cylinder was achieved by introducing small volumes (approximately 0.5 ml in 0.5 ml). At each experimental point the water temperature was measured with the help of the liquid glass thermometer. Additionally, atmospheric pressure and ambient temperature were measured (manufacturer: Forecast;

Range: 0 a 9999 mbar; Resolution: 1 mbar). The objective of increasing the volume of the graduated cylinder in small volumes was to reduce the impact of non-homogeneity related to the internal diameter.

At the end of this process, the scale calibration started again, however, in this situation, the tare function was not applied. Once the calibration of the balance was finished, the calibration of the graduated cylinder was carried out without discounting its initial mass (that is, without applying the tare function). The calibration procedure of the graduated cylinder followed the one described above. In both cases where the graduated cylinder was calibrated, 91 experimental points were obtained, to total the maximum volumetric capacity of 50 ml. Figure 2 illustrates a flow chart related to the methodology adopted in the research carried out. 

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To the Faculty of Sciences (Universidad del Atlántico), for to make available Laboratories, Materials and Non-Automatic Weighing Instruments. Thus, it was possible to realize the experiment procedure of the undergraduate project of the Department Mechanical Engineering: Experimental study of the influence of the tare function on an analytical balance for the calibration of volumetric meters.

The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the work reported in this article.