Indirect Determination of the Internal Diameter of Glass Conical Volumetric Instruments
Article Sidebar
Main Article Content
Abstract
Purpose: To determine the values of the internal diameter in conical-shaped glass volumetric instruments using height measurements, without needing to measure the wall thickness of the volumetric container, which will allow calculating the contribution to the uncertainty of volume measurement due to the adjustment of the meniscus.
Methodological design: The proposed method approximates volume by a series of truncated cones bounded by instrument graduation lines. The series of truncated cones thus defined is subject to comply with a geometric restriction. Then, for the graduation lines of the volumetric instrument that did not adhere to the constraint, a power regression model allows approximation of the value of the internal diameter.
Results: The proposed approach could be used as an alternative method to determine the internal diameter of glass conical volumetric instruments in cases where using a vernier caliper or optical comparator is not an option, either because the geometry of the conical instrument does not allow it or because higher cost instruments are not available.
Research limitations: Only two types of conical volumetric instruments were tested: an Imhoff cone and a centrifuge tube, with scopes of 1 L and 100 mL, respectively, from only two commercial brands of laboratory glassware. The volume of the tip of the instrument was modeled up to the first graduation mark, always as a semi-ellipsoid of revolution.
Findings: Comparing the direct measurement of the internal diameter of the volumetric instruments with an optical comparator, there is an average relative error below 10 %, with a maximum value below 20 % for the two different conical glass instruments studied.
Downloads
Article Details
Citas en Dimensions Service
References
Aisyah, L., Bethari, S.A., Wibowo, C.S., Hermawan, N., Alwi, D.U., Rulianto D., Anggarani, R. ( 2019). Water content in biodiesel for diesel fuel blends: measurement using centrifuge and coulometric titration method. IOP Conference Serires: Materials Science and Engineering. 494, pp. 1–5. DOI: 10.1088/1757-899X/494/1/012082
Arturi, T.S., Seijas, C. J., Bianchi, G. L. (2019). A comparative study on the treatment of gelatin production plant wastewater using electrocoagulation and chemical coagulation. Heliyon 5(5) e01738. DOI: 10.1016/j.heliyon.2019.e01738
American Society for Testing and Materials [ASTM] (2018). Standard Test Method for Water in Petroleum Products and Bituminous Material by Distillation (D95-13). Recuperado de: https://img.antpedia.com/standard/files/pdfs_ora/20211203/ASTM%20D95-13(2018).pdf
American Society for Testing and Materials [ASTM]. (2011). Standard Test Method for Water and Sediment in Fuel Oils by the Centrifuge Method (Laboratory Procedure) ( D1796-11). Recuperado de: https://www.astm.org/d1796-22.html
American Society for Testing and Materials [ASTM]. (2012). Standard Practice for Calibration of Laboratory Volumetric Apparatus (E542-01), Recuperado de: https://www.astm.org/e0542-01r21.html
Asociación Europea de Institutos Nacionales de Metrología [EURAMET] (2018) Calibration Guide Guidelines on the determination of uncertainty in gravimetric volume calibration. (3) Braunschweig, Germany: EURAMET. Recuperado de: https://www.euramet.org/publications-media-centre/calibration-guidelines
Batista, E.; Almeida, N.; Filipe, E. (2009). Uncertainty analysis in calibration of standard volume measures. In Pavese, F.; Bär, M.; Forbes, A. B.; Linares, J. M.; Perruchet, C.; Zhang, N. F. (eds.) Advanced Mathematical and Computational Tools in Metrology and Testing VIII (78) (pp. 28-31). Singapore: World Scientific Publishing Company.
Beer, F. P., Johnston, E., Mazrek, D. F., Cornwell, P. J., and Self, B. P. (2018). Vector Mechanics for Engineers (12th ed.) New York: McGraw-Hill.
Belgacem, L.; Cherif, R.A. (2023). Laboratory glassware cleaning validation in pharmaceutical industry: a case study. Accred Qual Assur 28, pp. 59-–64.DOI: 10.1007/s00769-023-01531-4
Biazon, C. L., Jesus, V. C., de Oliveira, E. C. (2015). Metrological Analysis by Measurement Uncertainty of Water and Sediment in Crude Oil. Petroleum Science and Technology. 33 (33), pp. 344-352.DOI: 10.1080/10916466.2014.980000
Boineau, F.; Plimmer, M. D.; Mahé, E. (2020). Volume calibration using a comparison method with a transfer leak flow rate. Acta IMEKO 9, pp. 343–348. DOI: https://doi.org/10.21014/acta_imeko.v9i5.997
Burgess, I. (2022, December 17) The surprising and significant errors in reading a centrifuge tube. https://validere.com/the-surprising-and-significant-errors-in-reading-a-centrifuge-tube
Chapra, S. C., and Canale, R. P. (2021). Numerical Methods for Engineers (8th ed.) New York: McGraw-Hill.
Deutsches Institute für Norming [DIN]. (2001). Laboratory glass or plastics ware - Imhoff sedimentation cones (DIN 12672:2001-10). Recuperado de: https://www.normadoc.com/spanish/din-12672-2001-10.html
Gupta, S. V. (2006). Comprehensive volume and capacity measurements. New Delhi: New Age International Publishers.
International Organization for Standardization [ISO]. (2015). Laboratory glass and plastics ware - Principles of design and construction of volumetric instruments (ISO 384:2015). Recuperado de: https://www.iso.org/standard/63918.html
International Organization for Standardization [ISO]. (2005). Laboratory glassware – Burettes (ISO 385:2005). Recuperado de: https://www.iso.org/standard/38678.html
International Organization for Standardization [ISO]. (2008). Laboratory glassware - Single-volume pipettes (ISO 648:2008). Recuperado de: https://www.iso.org/standard/44142.html
International Organization for Standardization [ISO]. (2007). Laboratory glassware - Graduated pipettes (ISO 835:2007). Recuperado de: https://www.iso.org/standard/41794.html
International Organization for Standardization [ISO]. (1998). Laboratory glassware - One-mark volumetric flasks (ISO 1042:1998). Recuperado de: https://www.iso.org/standard/25484.html
International Organization for Standardization [ISO]. (2010). Laboratory glassware - Volumetric instruments - Methods for testing of capacity and for use (ISO 4787:2010), Recuperado de: https://www.iso.org/standard/41807.html
International Organization for Standardization [ISO]. (2015). Quality management system – Requirements (ISO 9001:2015). Recuperado de: https://www.iso.org/standard/62085.html
International Organization for Standardization [ISO]. (2012). Geometrical product specifications (GPS) – Dimensional measuring equipment; Height gauges – Design and metrological characteristics (ISO 13225:2012). Recuperado de: https://www.iso.org/standard/42893.html
International Organization for Standardization [ISO]. (2015). Environmental management system - Requirements with guidance for use (ISO 14001:2015). Recuperado de: https://www.iso.org/standard/60857.html
International Organization for Standardization/ International Electrotechnical Commission [ISO/IEC]. (2012). General requirements for the competence of testing and calibration laboratories (ISO/IEC 17025). Recuperado de: https://www.iso.org/publication/PUB100424.html
International Organization for Standardization [ISO] 20461. (2000). Determination of uncertainty for volume measurements made using the gravimetric method (ISO/TR 20461). Recuperado de: https://www.iso.org/standard/34183.html
Liang, D., Steinert, C., Bammesberger, S., Tanguy, L., Ernst, A., Zengerle, R., Koltay, P. (2013). Novel gravimetric measurement technique for quantitative volume calibration in the sub-microliter range. Measurement Science Technoly 24 (2), pp. 1–10. DOI: 10.1088/0957-0233/24/2/025301
Liu, X; Bamberg, S. J. M.; Bamberg, E. (2011). Increasing the accuracy of level-based volume detection of medical liquids in test tubes by including the optical effect of the meniscus. Measurement 44 (4), pp. 750–761. DOI: https://doi.org/10.1016/j.measurement.2011.01.001
Lorefice, S. (2009). Traceability and uncertainty analysis in volume measurements. Measurement 42 (10), pp. 1510–1515. DOI: https://doi.org/10.1016/j.measurement.2009.07.016
Mandal, G., Kumar, A., Mandal, S., Sharma, D. C., and Kumar, M. (2019). Volume measurement of large volumetric vessel using tap water. MAPAN 34, pp. 487–493. Recuperado de: https://link.springer.com/article/10.1007/s12647-019-00319-7
Ortiz, E.G., Quintero, I., Arévalo, K. (2016). Biodiesel production from three mixes of oils with high free fatty content: quality evaluation and variable analysis. Int. J. Envirom. Sci. Technol. 13, pp.1367–1376. DOI: 10.1007/s13762-016-0980-9
Purata-Sifuentes, O-J., González-Gómez, H-L., Echavarri-Rodríguez, J-A., and Funes-Rodríguez, E. (2018). Estimation of meniscus reading uncertainty in volume calibration of conical volumetric instruments. Journal Physics; Conference Serires 1065, 092021. DOI: 10.1088/1742-6596/1065/9/092021
Purata-Sifuentes, O-J., González-Gómez, H-L., Echavarri-Rodríguez, J-A., and Funes-Rodríguez, E. (2021). Uncertainty Due to Meniscus Reading on Conical Graduated Volumetric Instruments. IEEE Access, 9, pp. 147801-147808. DOI: 10.1109/ACCESS.2021.3123961.1065:092021.
R Core Team (07 January 2023). The comprehensive R Archive Network. Recuperado de: http://CRAN.R-project.org/
Salsbury, J. G. (2022). Test uncertainty. Guide to the evaluation of measurement uncertainty in the conformity assessment of measuring instruments. Illinois, USA: Mitutoyo.
Win, M. L. (2021). Uncertainty of factor Z in gravimetric volume measurement. Acta IMEKO 10, pp. 198–201. DOI: https://doi.org/10.21014/acta_imeko.v10i3.1125
Zumdahl, S. S.; Zumdahl, S. A.; Hall, J. (2014). Lab Manual Experimental Chemistry (9th ed.) Belmont: Cengage Learning.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Entreciencias: Diálogos en la Sociedad del Conocimiento recognizes and respects the moral rights of authors as well as ownership rights transferred in non-exclusivity to the journal for its open access dissemination and its preservation. Hence, authors who publish in this journal accept the following conditions:
- Entreciencias: Diálogos en la Sociedad del Conocimiento from Universidad Nacional Autónoma de México is distributed under a Licencia Creative Commons Atribución-NoComercial-SinDerivar 4.0 Internacional, which allows the information and metadata to be used without commercial ends as long as proper citation is utilized.
Authors will have the right to non-exclusively distribute the contribution made to Entreciencias: Diálogos en la Sociedad del Conocimiento. That is, they will be able to include it in an institutional repository or disseminate it in other digital or printed media as long as it is explicitly stated that it was first published in Entreciencias: Diálogos en la Sociedad del Conocimiento. The following information must additionally be included: author, year, volume, page numbers, electronic paging, and DOI.
Authors, whose publications have been accepted, will have to send the Letter of Copyright Transfer in the corresponding format, filled out and signed by the author or authors.