Velocity and density scaling at the outlet of a silo and its role in the expression of the mass flow rate

The role of density and velocity profiles in the flow of particles through apertures has been recently put on evidence in a two-dimensional experiment (Phys. Rev. Lett. 108, 248001). For the whole range of apertures studied, both velocity and density profiles are selfsimilar and the obtained scaling functions allow to derive the relevant scales of the problem. Indeed, by means of the functionality obtained for these profiles, an exact expression for the mass flow rate was proposed. Such expression showed a perfect agreement with the experiential data. In this work, we generalize this study to the three dimensional case. We perform numerical simulations of a 3D silo in which the velocity and volume fraction profiles are determined. Both profiles shows that the scaling obtained for 2D can be generalized to the 3D case. Finally, the scaling of the mass flow rate with the outlet radius is discussed.