Hydraulic jumps on an incline

TL;DR

This paper investigates the behavior of hydraulic jumps on inclined surfaces, combining experiments and a simple theoretical model to understand the maximum rise height of fluid and its dependence on jet velocity and inclination.

Contribution

It provides the first experimental data and a simple theoretical framework for hydraulic jumps on inclined surfaces, focusing on maximum rise height and scaling laws.

Findings

Experimental measurements of maximum rise height

A simple theory based on horizontal hydraulic jumps

Scaling laws for rise height with jet velocity and inclination

Abstract

When a fluid jet strikes an inclined solid surface at normal incidence, gravity creates a flow pattern with a thick outer rim resembling a parabola and reminiscent of a hydraulic jump. There appears to be little theory or experiments describing simple aspects of this phenomenon, such as the maximum rise height of the fluid above the impact point, and its dependence on jet velocity and inclination angle. We address this with experiments, and present a simple theory based on horizontal hydraulic jumps which accounts for the rise height and its scaling, though without describing the shape of the parabolic envelope.