Circular hydraulic jump in generalized-Newtonian fluids

TL;DR

This paper analytically investigates laminar circular hydraulic jumps in generalized-Newtonian fluids using a power-law model, deriving exact flow expressions and jump radius relations, extending classical Newtonian results.

Contribution

It provides the first analytical framework for circular hydraulic jumps in non-Newtonian fluids with explicit formulas and jump radius relations, generalizing Newtonian cases.

Findings

Exact flow expressions for generalized-Newtonian fluids.

Implicit relation for the jump radius.

Predictions for non-Newtonian fluid behavior.

Abstract

We carry out an analytical study of laminar circular hydraulic jumps, in generalized-Newtonian fluids obeying the two-parametric power-law model of Ostwald-de Waele. Under the boundary-layer approximation we obtained exact expressions determining the flow, an implicit relation for the jump radius is derived. Corresponding results for Newtonian fluids can be retrieved as a limiting case for the flow behavior index n=1, predictions are made for fluids deviating from Newtonian behavior.