Experimental Insights into Hydraulic Jump Roller Length: The Impact of Compound Geometry, Slope, and Bed Roughness

Abstract

This experimental investigation examines the relative roller length (Lr/h1) of hydraulic jumps taking place in composite rectangular channel featuring positive inclinations and roughened minor beds, aiming to address gaps in understanding the effects of channel geometry, slope, and bed roughness. Experiments were conducted in a laboratory flume with a main channel width of 25 cm and a minor bed width of 14.4 cm. The experimental variables included channel slope (tan(α) = 0 to 0.015), bed roughness (ε = 0 to 12 mm), sill height (h_s = 2.5 to 21 cm), and inlet flow depths (hs = 2.5–4 cm), producing Froude number ranging from 1.5 to 9 and Reynolds number between approximately 24500 and 1025000. Results demonstrate that increasing bed roughness reduces the relative roller length by 21–29%, thereby enhancing turbulence and energy dissipation, while positive slopes stabilize hydraulic jumps by promoting smoother flow transitions. A novel dimensionless empirical model relating Lr/h1 to F1, tan(α), and relative roughness (ε/b) was developed and validated, exhibiting high accuracy (R2 = 0.99) with predictions within ±5% of experimental values. This model provides a robust predictive tool for hydraulic structure design, enabling reductions in stilling basin dimensions by 23–28% while maintaining equivalent energy dissipation, yielding significant cost (17–22%) and space savings. These findings address critical gaps in understanding hydraulic jump dynamics in complex channel geometries and offer practical insights for designing energy dissipators, spillways, and flood control infrastructure to enhance flow stability, efficiency, and sustainable water management.