Hydraulic jumps play a critical role in dissipating flow energy downstream of hydraulic structures, yet optimizing their efficiency in complex geometries like stepped weirs remains a challenge. This study investigates the energy dissipation characteristics of hydraulic jumps formed downstream of novel cylindrical stepped weirs, focusing on the interplay between weir geometry and flow dynamics. A total of 27 physical models were tested in a laboratory flume, systematically varying weir heights (P = 30, 45, 60 cm), step diameters (D = 2.5, 5, 7.5 cm), and step configurations: fully circular steps (Fc), mixed circular and half-cut steps (Fc & Hc), and fully half-cut steps (Hc), all at a fixed slope (θ = 45°). Using dimensional analysis and statistical modeling (R 2 = 0.968), energy dissipation was correlated with geometric and hydraulic parameters. Key findings reveal that energy loss increases by 29.4% when step diameter decreases from 7.5 cm to 2.5 cm, and by 7.8% when step count rises from 12 to 24. The fully circular configuration (Fc) achieved the highest dissipation (72.4%) at P = 60 cm, D = 2.5 cm, and Fr 1 = 9, outperforming Hc by 13.2%. Energy dissipation was also scaled with Froude number (Fr 1 ) and depth ratio (y 2 /y 1 ), while smaller step diameters reduced hydraulic jump length by 18.7%, enabling compact stilling basin designs. These results demonstrate that cylindrical stepped weirs with optimized geometry significantly enhance energy dissipation efficiency, providing actionable insights for sustainable hydraulic structure design in flood control and dam safety applications.
Mohammed et al. (2026) studied this question.