Characteristics of a hydraulic jump in Bingham fluid

TL;DR

This study develops a macroscopic model for hydraulic jumps in Bingham fluids, providing approximate formulas for conjugate depths and shear stress with verified accuracy, enhancing understanding of flow behavior in such non-Newtonian fluids.

Contribution

The paper introduces an approximate formula for conjugate depths in Bingham fluids' hydraulic jumps, with less than 4% error, and analyzes shear stress variations.

Findings

Critical depth and conjugate depth ratio increase then decrease after a certain shear stress threshold.

Downstream shear stress is smaller than upstream shear stress.

Approximate formulas are validated with experimental data.

Abstract

In this paper, we seek an adequate macroscopic model for a hydraulic jump in Bingham fluid. The formulas for conjugate depths, sequent bottom shear stress and critical depth are established. Since no exact analytical solution in closed form is available for conjugate depths, an approximate formula is developed. This formula can provide good results with an error less than 4%. The analytical results have revealed that the critical depth and the ratio of conjugate depths increase until bottom shear stress exceeds a certain value and then decrease afterwards. The bottom shear stress downstream of the jump is smaller than that upstream. The results are verified by experimental data and observations available in the literature.