Empirical analysis of hydraulic jump roller length in sloped composite channels with different roughness coefficients

The hydraulic jump is a fundamental transitional phenomenon between supercritical and subcritical flow in open channels, playing a pivotal role in stabilizing hydraulic systems, dissipating energy, and preventing scour downstream of hydraulic structures. This study investigates the combined effects of channel slope and major bed roughness in a rectangular compound channel on hydraulic jump characteristics. Laboratory experiments were conducted using a 10‑meter flume equipped with adjustable longitudinal slopes and roughened surfaces of varying diameters. The study focused on determining the relative roller length (Lr/h1) under different upstream Froude numbers, slopes, and roughness conditions. Results show that the relative roller length increases with the Froude number but decreases with increasing bed roughness. A global predictive equation was developed, integrating Froude number, slope, and roughness, which demonstrated excellent agreement with experimental data (R² = 0.9985) and low error margins. This confirms the robustness of the model and its potential for practical application in the design of stilling basins and hydraulic energy dissipation systems.