Analysis of quantitative expression of viscous coefficient for sediment-laden flow

Abstract

The modified viscous coefficient of non-uniform sediment-laden flow based on Zhu Junda's theoretical equation is generally utilized in the calculation mode of hyper-concentrated flow at present. Nevertheless, the gradation conservation of nonuniform sediment was neglected in the theoretical derivation with the irrational loss of fine sediment. The assumed replacement conditions in the derivation resulted in the coarsening effect of suspended sediment gradation in muddy water. Meanwhile, the degree of particle coarsening would be more serious with the increasing replacement times of micro-volume of sediment groups. The computed result of Zhu Junda's equation would underestimate the viscosity of sediment-laden water. Furthermore, the magnitude and velocity of deviation increment for the equation are reckoned. Compared Einstein's viscosity formula with the Taylor Series expansion of Zhu Junda's equation, the Einstein's formula with strong limitations is not a special case. In accordance with suspended sediment gradation, this paper brings in the displacement factors varying with sediment particles, and corrects the defects in the derivation of theoretical formulas about viscous coefficient. On the basis of Einstein classical formula, the quantitative relationship between the viscosity coefficient of muddy water and the sediment concentration is obtained. Moreover, Einstein classical formula is the special case of this quantitative expression. The applicability and limitation of the deduced formula for calculating viscous coefficient are verified and discussed with the data gained from the viscosity measurement experiments.