# METHODOLOGY OF CALCULATION THE TERMINAL SETTLING VELOCITY DISTRIBUTION OF SPHERICAL PARTICLES FOR HIGH VALUES OF THE REYNOLD’S NUMBER

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## Abstract

The particle settling velocity is the feature of separation in such processes as flowing classification and jigging. It characterizes material forwarded to the separation process and belongs to the so-called complex features because it is the function of particle density and size. i.e. the function of two simple features. The affiliation to a given subset is determined by the values of two properties and the distribution of such feature in a sample is the function of distributions of particle density and size. The knowledge about distribution of particle settling velocity in jigging process is as much important factor as knowledge about particle size distribution in screening or particle density distribution in dense media beneficiation.

The paper will present a method of determining the distribution of settling velocity in the sample of spherical particles for the turbulent particle motion in which the settling velocity is expressed by the Newton formula. Because it depends on density and size of particle which are random variable of certain distributions, the settling velocity is a random variable. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity for the turbulent motion and particularly calculate probability density function for Weibull’s forms of frequency functions of particle size and density. Distribution of settling velocity will calculate numerically and perform in graphical form.

The paper presents the simulation of calculation of settling velocity distribution on the basis of real distributions of density and projective diameter of particles assuming that particles are spherical.

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# Archives of Mining Sciences

## The Journal of Committee of Mining of Polish Academy of Sciences

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