Hydraulic jump analysis for a Bingham fluid

Abstract

A theoretical study of the hydraulic jump in a Bingham fluid is presented in this paper. Based on the approximation for lubrication theory, the formulae for conjugate depths, sequent bottom shear stress and critical depth are established. Due to the absence of an exact solution of the basic equations for conjugate depths, an analytical approximation has been developed. This formula is shown to provide good results, with a small error of less than 4%. The analytical results have revealed that the critical depth and the ratio of conjugate depths increase until the bottom shear stress reaches a certain value and decreases above that. Both the critical depth and the ratio of conjugate depths have maximum values where the critical flow or the jump is coupled between the effects of shear-free and shear regions. Reasonable agreement is achieved between the theoretical results and experimental data for conjugate and critical depths. The observation that the critical depth increases greatly when the dimensionless yield stress λ ≥ 0.1 in the experiment provides further justification for the theoretical approach