Minerals Beneficiation - The Development of Formula for Direct Determination of Free Settling Velocity of Any Size Particle

An equation has been developed which will permit the direct determination of free settling velocity of any sized particle encountered in mineral benefici-ation. The equation is based on Newton's Law with the friction factor defined as a function of the laminar boundary layer. Development of the equation is described first from an empirical trial-and-error approach. Examples are given of actual settling data from the literature versus calculated data to prove the validity of the new equation. Newton's law of resistance of a fluid to flow around a sphere is expressed in Eq. 1. Free settling velocities can be determined by setting Eq. 1 equal to the gravitational force on a particle and solving for V. Experience has shown that when the solids are greater than 1 mm in diam, or when Reynold's number for the system is greater than 800-1000, the friction factor term, fD, essentially becomes a constant, and Eq. 2-b becomes Newton's equation for free-settling and is applicable under the conditions stated. Another special condition exists for particles smaller than 0.05 mm or when Reynold's number for the system is less than three. In this case fD=24/NRor24µ/pL,dV,. Eq. 2-b can then be rewritten as