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A theoretical analysis of velocity profiles in sediment-laden flows is presented by means of Prandtl-Karman mixing length theorem. The study shows that the upward velocity of liquid-phase caused by settling sediment leads to the invalidity of the log-law and Rouse equation. The theoretical analysis takes into account the upward velocity and shows: 1) the mean velocity in sediment-laden flows follows the log-law, but the Karman constant reduces in the main flow region, 2) sediment concentration reduces the mixing length of fluid particles, 3) flow resistance reduces with the presence of sediment concentration, and 4) the sediment concentration profile deviates from the well know Rouse equation. The experimental data agree well with the equations derived on the basis of non-zero wall velocity. It is found that the wall-normal velocity should not be neglected for density gradient flows because it induces more than for pure water flows.
A theoretical analysis of velocity profiles in sediment-laden flows is presented by means of Prandtl-Karman mixing length theorem. The study shows that upward velocity of liquid-phase caused by settling sediment leads to the invalidity of the log-law and Rouse equation The theoretical analysis takes into account the upward velocity and shows: 1) the mean velocity in sediment-laden flows follows the log-law, but the Karman constant reduces in the main flow region, 2) sediment concentration reduces the mixing length of fluid particles, 3) flow resistance reduces with the presence of sediment concentration, and 4) the sediment concentration profile deviates from the well know Rouse equation. The experimental data agree well with the equations derived on the basis of non-zero wall velocity. It is found that the wall-normal velocity should not be neglected for density gradient flows because it induces more than for pure water flows.