Flows from Bins: New Results - Selected Topics of Computational and Experimental Fluid Mechanics - page 160

Fig. 6 Left hand side Charles-Agustin Coulomb. Right hand side Coulomb's publication by 1773

depend on the true contact area—a much more intuitively satisfying argument than
what the Amontons-Coulomb law allows. Bowden and Tabor argued that within these
asperities all of the dynamics of friction take place.
Despite the substantial advance of the inclusion of friction into granular material
problems, the physics of friction processes still remains insufficiently clear because
there still remain a lot of unsolved questions in problems such as wear and heating of
materials in friction, the distribution of normal and tangential stresses in the contact
region, plastic deformations, and the physical nature of frictional forces (molecular
adhesion, hysteresis losses, losses in the case of surface layer failure, etc.) (See, for
instance, Zhuravlev 2013 ).

3 The Mass Flow Rate Problem

The silo discharge through a bottom circular outlet, the granular analogous of the
Torricelli's theorem, is one of the oldest andmost widely studied problems in granular
flow owing to the simple setup and geometry of the system (Brown and Richards
1970 ; Beverloo et al. 1961 ; Franklin and Johanson 1955 ; Hagen 1852 ; Wieghardt
1975 ). It has been extensively investigated both experimentally and computationally.
Today, many granular, gravity flow theories use silo discharge as a benchmark for
validation (Brown and Richards 1970 ). Conversely, the study of the mass flow rate