A Semi-Theoretical Study on the Effect of Rough Beds on the Conjugate Depth Ratio in Hydraulic Jumps

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This study examines the effects of bed roughness on hydraulic jump characteristics in rectangular composite channels. Experiments were conducted in a laboratory flume with two roughness zones: the main channel and the floodplain, using uniform plastic granules to simulate different roughness conditions. The results show that increased bed roughness significantly reduces the subsequent depth ratio. A semi-theoretical dimensionless approach was developed to analyze the hydraulic jump, incorporating key parameters, such as the incident Froude number, the resistance coefficient, the expansion ratio, the shape factor, and the conjugate depth ratio. This approach, based on Euler's theory applied between two sections of the hydraulic jump, allows the conjugate depth ratio to be predicted using the flow rate and the tested absolute roughness values. The experimental validation confirms the accuracy of this model in estimating the conjugate depth ratio under varying roughness conditions. The developed approach provides a practical tool for engineers to optimize hydraulic structures in channels with variable roughness and zero slope, improving flow regulation and reducing erosive forces.

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