Using discrete simulations of granular flows on smooth inclines bounded by smooth lateral walls, we confirm recent findings indicating that the local effective wall friction can be described by a simple law involving a single Froude-like dimensionless number—defined as the ratio of the slip velocity to the square root of the wall pressure. This relationship has been validated for a fixed gap width $W$ across a wide range of inclination angles and mass hold-up values. Remarkably, it holds in both steady, fully developed regimes and in unsteady flow conditions. We also establish a similar empirical law governing the local packing fraction at the wall. Notably, the Froude number proves to be a reliable proxy for the ratio of the slip velocity at contact to the square root of the granular temperature. Together, these relationships for wall friction and packing fraction provide general boundary conditions for granular flows confined by flat frictional surfaces. Our results also highlight the significant influence of lateral walls, which induce pronounced differences between the velocity profiles near the walls and those at the flow center. Furthermore, the tensorial form of the $\mu \left(I\right)$ rheology generally fails to capture the flow behavior, except near the centerline. In contrast, the kinetic theory of granular gases offers a more suitable framework for describing the observed flow dynamics. Finally, we exploit spatially averaged versions of the wall friction and packing fraction laws to construct a depth-averaged model that successfully predicts the basal-averaged velocity of granular flows on a flat frictional base, laterally bounded by flat frictional walls.

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• Granular flows