Prediction of hopper discharge rates of binary granular mixtures

Measured flowing densities of binary mixtures of equal-solids density near-spherical granules discharging from a hopper are correlated with static densities calculated using the linear-mixture packing model developed by Yu and Standish. This correlation is used in a modified form of the Beverloo equation to predict the rate of discharge of solid materials through a hopper orifice. The so-called 'empty annulus' effect in the modified Beverloo equation is related to statistical mean particle sizes representing binary mixtures. A general equation is developed in two forms, the first is universal, encompassing both segregating and non-segregating systems, and the second is specific to non-segregating systems. They can be used to calculate hopper discharge rates for binary mixtures without need for experimental data. Both are found to correlate closely with experimentally measured discharged rates.