Mathematical models describing the flow of granular material

Models used to describe the flow of granular material through orifices has been under review for a long period of time. The need for a model that accurately describes the gravity flow of a wide variety of granular materials is greatly needed for the design of equipment such as grain drills, storage bins, and others used in all types of industries. In addition to only having a model that predicts flow, the model should have a physical basis so that the laws governing flow is known. Four different models have been reviewed, tested, and evaluated for the level at which each predicts the flow of granular material through circular orifices. Material with a bulk density ranging from 0.1 to 0.9 g/cm³ were used in the evaluation. All orifices tested were circular and horizontal with sizes ranging from 1.3 to 10.5 cm, and flow was by gravity only. Comparison of the results showed that the goodness of fit as measured by R² ranged from 0.30 to 0.99, with a significance level as high as 99.9 percent (α = 0.001). Of the models tested, two showed excellent results: the Gregory and Fedler (1987) model and the Beverloo et al. (1961) model.