We outline an extension of the hydrodynamic equations for dense flows of identical, inelastic spheres that incorporates an additional length scale in the expression for the collisional rate of dissipation. This length scale is identified with the length of a particle chain. In steady, fully developed inclined flows, the resulting theory predicts that at a given angle of inclination a range of flow depths is possible, that such flows possess a region of uniform volume fraction, and that this volume fraction decreases as the angle of inclination increases. The balance of particle fluctuation energy, integrated through the depth of a flow, results in a relation between the mean flow velocity, the depth, and the angle of inclination that collapses experimental data taken over a range of inclination angle.
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