Unified laws of velocity distribution for sediment laden flow with high and low concentration

As a typical solid and liquid phase flow existing universally in the nature, it is well-known that the velocity distribution laws of sediment laden flow is different from those of clear water flow. By means of velocity measurements for sediment laden flow in the natural sand tests, the characteristics of turbulent flow with high and low concentration has been analyzed comprehensively in this paper. Furthermore, according to basic logarithm formula of velocity distribution, unified formula of Karman constant κ for the flow with high and low concentration has been reasonably expressed by using relative viscosity index μ_r to be related to concentration and grain diameter distribution. Finally, by comparing and verifying for two kinds of velocity formulas, the unified laws of logarithm velocity distribution with both Karman-Prandtle velocity and Karman constant κ has been analyzed and verified by using measured velocity data in the coal powder tests. The achieved results above are significant for revealing water flowing structure and sediment transporting mechanism, enriching river mechanics and guiding river harnessing engineering.