# Features of calculation arch support with a splitting investigation of the final deposition rates in liquids of elongated rock particles

Wet gravity processes of ore separation are characterized by greater environmental friendliness compared to dry methods of enrichment. They allow you to separate rocks taking into account the size, density and shape of the grains. The practice of enrichment has shown that the grains of most ores after crushing and grinding differ significantly in shape from each other. Practically all the theoretical foundations of gravitational separation have been developed for spherical particles and, when applied to cylindrical forms, require clarification and appropriate corrections. The article provides an analysis of existing methods for determining the velocity of falling particles in a liquid. A method for determining the steady-state velocity of cylindrical particles of elongated shape taking into account the position of the particle is given. As a result of the research, it was found that for cylindrical particles, the area of the Mid-section varies depending on its position when falling randomly from the area of a circle to a rectangle. The results of experiments to determine the steady-state velocity of cylindrical particles of elongated shape in water, depending on the ratio of particle length to diameter, are presented. Graphs of the dependence of the velocity of falling particles with a density of 1.27 g/cm3 in water on the ratio of their length to diameter are given. The statistical dependence of the velocity of falling particles in water on the ratio of their length to diameter is found. The necessity of developing a simulation model of the process taking into account the random nature of particle sizes: length, diameter, as well as the angle between the longitudinal axis of symmetry of the particle and the velocity vector of the particle “α” is substantiated. Moreover, when developing a model, it is necessary to take into account the type of laws of distribution of random variables.

Keywords: the velocity of falling particles in a liquid, the Reynolds number, the diameter and length of the particle, the mid-section, the coefficient of resistance of the medium.
For citation:

Afanas’ev A. I., Potapov V. Ya., Uporov S. A., Potapov V. V. Features of calculation arch support with a splitting investigation of the final deposition rates in liquids of elongated rock particles. MIAB. Mining Inf. Anal. Bull. 2023;(12-1):5—16. [In Russ]. DOI: 10.25018/0236_1493_2023_121_0_5.

Acknowledgements:
Issue number: 12
Year: 2023
Page number: 5-16
ISBN: 0236-1493
UDK: 622.5:621.928.46
DOI: 10.25018/0236_1493_2023_121_0_5
Article receipt date: 15.05.2023
Date of review receipt: 09.11.2023
Date of the editorial board′s decision on the article′s publishing: 10.11.2023

Afanas’ev A. I.1, Dr. Sci. (Eng.), professor of the department of technical mechanics, http:// orcid.org/0000−0002−7869−9208 Е-mail: anatoly.afanasiev1948@yandex.ru
Potapov V. Ya.1, Dr. Sci. (Eng.), professor of the department of mining mechanics, http:// orcid.org/0009−0003−0305−5349, Е-mail: 2с1@inbox.ru
Uporov S. A.1, Cand. Sci. (Eng.), vice-rector for educational and methodological complex, http://orcid.org/0009−0008−8897−1480, Е-mail: UporovSA@m.ursmu.ru,
Potapov V. V.1, Cand. Sci. (Eng.), associate professor of the department of mining, http:// orcid.org/0000−0003−4862−523X Е-mail: actusprimo@gmail.com
1 Ural State Mining University, Russia, 620144, Yekaterinburg city, Kuibyshev st. 30.

For contacts:
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