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|A mathematical model is presented which allows the free or hindered settling velocity to he calculated for any size or- shape particle in any fluid, and at any percent solids up to the maximum. The validity of the model is supported by comparing calculated velocities (or viscosities) with measured values for 1073 data points contained in 80 sets of data encompassing a range of Reynolds’ numbers, from 0.002 to 770.000. The average error was 0.69%, with an average standard deviation of 6.65%. The derivation of the model is too lengthy to include in this paper, which will specifically present the application of the model to the free settling of minerals and spheres, prediction of the friction factor in wind tunnel tests, the viscosity of suspensions of spheres, the hindered settling of mono-sized spheres and closely sized minerals, and the settling of large spheres in suspensions of small spheres.|