An Experimental and Analytical Study of a Hydraulic Jump Over a Rough Bed with an Adverse Slope and a Positive Step

In this research, hydraulic jump characteristics were experimentally and analytically investigated on different adverse slopes, bed roughness, and positive step heights. The number of experiments was 576, which were carried out in Froude numbers ranging from 4 to 10. The results showed that the decrease in the sequent depth ratio and the increase in the relative energy loss were 33 and 27.41% more than those in the classic jump, respectively. Two new analytical solutions were developed using the momentum equation associated with other basic fluid mechanic equations for estimating the sequent depth ratio. Also, another new analytical solution was presented to estimate the relative energy loss as a function of the experiment conditions. The results also demonstrated that the maximum errors of the two analytical methods of estimating the sequent depth ratio were ± 15 and ± 20%, respectively. Further, the maximum error of estimating the relative energy loss was ± 11%. Given sufficient accuracy, using these analytical equations could be recommended for estimating the sequent depth ratio and the relative energy loss in order to prevent time and save costs.