Outflow properties of silos: The effect of arching

Engineers working on the field of agriculture, food- or pharmaceutical industry or in the architecture frequently meet problems arising from the special properties of granular assemblies. Storing large amount of particulate raw materials is mostly made by using large containers, called silos. The design of such large silos is far not an easy problem. The outflow properties are one of the most important parameters of silo design. The constant discharge rate of silos differs from the discharge rate of containers filled with liquids. In case of fluids, the flowing velocity and discharge rate changes with fluid level. In case of granular materials, the velocity is constant (independent of the filling level of silo). There are methods used for the determination of silo discharge rate, but these are mostly experimental without physical explanation of the phenomenon. In this paper we demonstrate that the constant discharge rate is caused by the formation and collapse of arches in the bin. Based on this assumption, we derive an equation for determining the discharge rate. Using the same arching hypothesis we derive the equations describing the velocity distribution at silo outlets. The usability of our new approach is demonstrated by experimental investigations.