A Mathematical Model for Conical Hopper Mass Efficiency

Almost every branch of industry, at a certain point, utilizes omnifarous materials in their granular form. A key constituent in many bulk material logistic systems is the hopper, which usually acts as a buffering component. In order to achieve the desired throughput, the geometry of the particular hopper must be carefully determined. Considering the geometric properties of the given hopper, the inclination of the walls and the outlet orifice characteristics are the pivotal determinants of hopper functionality. In this paper, the authors have developed an analytical model of the conical hopper’s mass efficiency and compared the model with the experimental results for two distinctive granular materials. The model inputs were: the density of the bulk material, critical angle of material repose, generatrix inclination angle of the cone, and diameter of the circular outlet. The experiment was conducted according to a 32 full factorial design. The repeatability of the results was examined according to Cochran’s theorem and the adequacy of the data was evaluated via Fisher’s criterion, which confirmed the quality of the mathematical model. The error of the developed model does not exceed 4.5%.