Theory of calculation of hopper outlets for hard-running materials

For many years in Russia and abroad research has been conducted on factors influencing the flow of various bulk materials from hoppers. On the basis of the research results, hopper designs are improved, the process of their unloading is mechanised and automated. In some industries of production there is a noticeable progress in this direction. However, there is a need for a solid basis for engineering calculations and design of hoppers. It concerns, in particular, to mixed fodder industry, where along with hoppers warehouses of floor type are used for storage of raw materials and finished products because of insufficient bulkiness of materials. Besides, in conditions of mixed fodder enterprises hoppers are an obligatory component of the mechanized lines used for reception, in-plant transportation, feeding into a production flow of various kinds of raw materials and shipment of finished products. The aim of the study is to theoretically justify and calculate the minimum permissible area of the outlet in the hopper for hard-running materials. The calculation is based on the model of a hard-running body, which is a continuous bulk medium. It is assumed that the flow of hard-running material from the hopper outlet becomes possible when the weight of the product layer above the outlet exceeds the force of external friction of the material against the vertical walls of the hopper; the force of external friction of the material against the inclined walls of the bottom; the force of transverse compression of the material layer in the outlet funnel. The calculation formula is derived from the equation of limit equilibrium. Determining the area of square face size or diameter of the outlet opening in the hopper using the formula will optimize the flow of hard-running materials, thereby increasing the efficiency of the process.