Hydraulic jump in sloping channels: roller length and energy loss

Abstract

This paper deals with the roller length and energy loss of a large variety of hydraulic jumps in horizontal and sloping channels. The supercritical upstream flow originated from a standard ogee weir. A stilling basin with bottom slopes of 0.0, -0.025, -0.050, -0.075, and -0.100 was used to generate the jumps. Based on the energy principle, a semiempirical method to predict the roller length is presented. Predictions based on the proposed method agree well with the results reported by the authors and other researchers. It is shown that the energy loss in the classical jump is greater than that in any jump forming on negative or positive slopes.Résumé : Cet article traite de la longueur des rouleaux et de la perte d'énergie d'une grande variété de ressauts hydrauliques dans les canaux horizontaux et en pente. L'écoulement surcritique en amont provenait d'un déversoir en doucine standard. Un bassin de tranquillisation muni de pentes de fond de 0,0, -0,025, -0,050, -0,075 et -0,100 a été utilisé pour générer les ressauts. Une méthode semi-empirique basée sur le principe de l'énergie est présentée afin de prévoir la longueur des rouleaux. Les prévisions basées sur la méthode proposée concordent bien avec les résultats rapportés par les auteurs et d'autres chercheurs. Il a été démontré que la perte d'énergie dans le ressaut hydraulique conventionnel est supérieure à celle de tout ressaut se formant sur des pentes négatives ou positives.Mots-clés : ressaut hydraulique, canal en pente, pente inverse, longueur de rouleau, perte d'énergie.[Traduit par la Rédaction]

Hydraulic Jumps in Adverse-Slope Stilling Basins for Stepped Spillways

“…On the other hand, results obtained with the method of [16] fail to account for the different apron slopes. Results obtained by method [19] adequately follow the trend of measured values. However, they are very scattered, with relative errors between −17% and +34%.…”

“…However, they are very scattered, with relative errors between −17% and +34%. Results obtained by [19] fail to account for different positions of the hydraulic jump. We hypothesize for methods [16,19] that the observed disagreements exist due to differences in experimental setups, the sensitivity of their equations, and their coefficients being problem dependent.…”

“…Results obtained by [19] fail to account for different positions of the hydraulic jump. We hypothesize for methods [16,19] that the observed disagreements exist due to differences in experimental setups, the sensitivity of their equations, and their coefficients being problem dependent. Table 3 shows that the incoming clear-water depth, h w1 , is underestimated by −1 to −5% with the method by [1,2] when compared to EC probe measurements.…”

“…Empirical expressions for F jumps were proposed by [3,16,17]. More recently, Beirami and Chamani [18,19] suggested a new type, called the B-F jump, which begins in the upstream channel of positive slope (spillway) and ends in the downstream channel of adverse (negative) slope. They stated that the B-F jump exhibits stable behavior and presented a momentum-based method for estimating the sequent depth ratio, the hydraulic jump length, and the energy dissipation efficiency for both F and B-F jumps.…”

Energy Dissipation in Eighteen-Foot Drop Broken-Back Culvert under Open Channel Flow Conditions

“…It was found that the negative slope of the basin reduced the sequent depth ratio, whereas a positive slope increased the sequent ratio. Also, Beirami and Chamani (2010) reported that the energy loss in the classical jump is greater than that in any jump forming on negative or positive slopes. Hartner et al (2003) stated that the characteristics of the hydraulic jump depend on Froude number (F r1 ).…”