Abstract
We present a new method to evaluate the hydraulic jump characteristics in a horizontal rectangular channel with a positive step. We considered the flow curvature effect and the free surface’s small rise at the A-type hydraulic jump’s end. First, we present a novel method to give jump length estimation based on the similarity of the jump and the turbulent wall-jet, considering the pressure gradient. Then, considering the jump as a curvilinear flow and using a one-dimensional momentum equation, we present an accurate expression for the conjugate flow depth regarding the initial Froude number and step height. Finally, we compute the jump’s energy dissipation rate. Compared to the theoretical models for conjugate flow depth in a hydraulic jump, the proposed equation in this study fit the experimental data better, even for high steps and large initial Froude numbers. However, for low Froude numbers (F1 < 5), the equation was less accurate in estimating the jump length. Regarding the jump’s energy dissipation rate, the results agreed well with the experimental data from previous investigations. However, it is noted that the increased energy dissipation rate dwindled in larger Froude numbers.
Highlights
Hydraulic jump has been widely used as an energy dissipater in stilling basin design.A more efficient stilling basin can be designed if the sequent depth is lower, jump length is shorter, and energy loss in the jump is higher than that in the classical jump [1]
According to Hager and Bretz [2], in a hydraulic jump, if the whole jump length occurs upstream of a positive step and ends at the step brink, it is classified as an A-type hydraulic jump (Figure 1)
A-type hydraulic jump a Thispaper paper presents presents a new jump in ainhorhorizontal rectangular channel with a positive step
Summary
Hydraulic jump has been widely used as an energy dissipater in stilling basin design. Where F1 is the initial Froude number; q is the unit discharge; g is the gravitational acceleration; h1 is the flow depth just before the jump; Y is the conjugate flow depth; h3 is the tail water depth; S is the relative step height; and s is the step height (Figure 1). Where F1 is the initial Froude number; q is the unit discharge; g is the gravitational 2accelof 10 eration; h1 is the flow depth just before the jump; Y is the conjugate flow depth; h3 is the tail water depth; S is the relative step height; and s is the step height (Figure 1). Froude number form for jumps at positive steps, in which channel and slope and step height effects are inserted separately. The heart of the present approximation relies on a quantity that can represent the non-hydrostatic pressure at the step section, along with the small rise of the jump free surface at the step brink
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