Indirect Determination of the Internal Diameter of Glass Conical Volumetric Instruments

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.