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The velocity of solid particles flowing in an inclined open channel of which the bottom plate was covered with very rough sandpaper was measured for three kinds of particle. Except for the region near the bottom plate, the velocity distribution normal to the bottom plate appeared to be linear. The velocity gradient in that region was almost independent of the thickness of the particle layer and increased as the slope of the channel became steep. These observed velocity distributions were analyzed based on the variational principle, by which the velocity distribution could be obtained as the solution which minimized a certain integral consisting of several energy terms. It was found that such analysis could explain the main feature of the particle flow in an inclined channel, and the following relation between stress and rate of deformation was obtained. τyz=kτy-kμy(dvz/dy) It was also found that the critical inclination angle of the channel, which was anticipated by the analysis, corresponded to the angle of repose.

Velocity distributions in the flow of solid particles in an inclined open channel.