Theoretical Modeling of Hydraulic Jumps at Negative Step in Radial Stilling Basins with End Sill

The hydraulic jump has been studied as an important method for energy dissipation downstream water structures. Several methods have been used to optimize the hydraulic jump length. One of the common methods was the use of end sill. Steps may be used to control the location of the hydraulic jump downstream of hydraulic structures. Extensive studies have been conducted to investigate the effect of steps in rectangular basins but not yet in radial basins. In the present paper, theoretical models are developed to predict the depth ratios of the radial hydraulic jumps at negative steps downstream of the control structures when the stilling basins is ended with a sill. Both the momentum and continuity equations in one dimension are applied to the control volume where the jump begins and ends. Both forms of the hydraulic jump (A and B) at negative step in the radial stilling basins are dealt. An experimental program is conducted to collect experimental data to enable verification of the developed theoretical models. Good agreement between theoretical and experimental results is obtained. The developed models are recommended for use in the design of radial stilling basin to compute the depth ratios which is needed to complete the dimensioning of the stilling basin.