We study steady, fully developed, axisymmetric flows of soft, inelastic grains within a vertical circular pipe under the influence of gravity. We use extended kinetic theory to describe the collisional flow and include a region above the critical solid volume fraction near the center line that is the analog of an erodible bed. We calculate the profiles of velocity, shear stress, granular temperature, and particle concentration across the pipe for a variety of volume flow rates and pipe radii. We compare these with those measured in discrete element simulations by Barker et al. [J. Fluid Mech. 930, A21 (2022)] and see good agreement.

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• Granular flows
• Granular materials