Gravity mass powder flow through conical hoppers ‐ Part II: A mathematical model predicting the axial and radial profiles of normal stresses from flow velocity measurements

In Part I of this work, a semi‐empirical equation was developed to predict the radial velocity profile of gravity‐driven, free‐flowing powders in conical hoppers. Phenomenological cohesion and adhesion parameters, such as friction angles as well as hopper angle, are the independent variables of this equation. This second part is an extension of the Janssen analysis predicting the axial profile of the applied normal stress. Force balances in cylindrical coordinates are performed for the conical gravity flows. The resulting partial differential equations are complemented by Newton's law, which links the normal stresses with velocity vectors presenting axial and radial components. The proposed model is in agreement with the available literature on normal stress profiles.