Proposed Equation to Estimate the Length of a Hydraulic Jump in a Rectangular Open Channel Hydraulic with Variable Slope, and Its Comparison with Seven Theoretical Equations of Specialized Literature

Abstract

A hydraulic jump is a localized phenomenon that generates on an open hydraulic channel; however, its mathematical demonstration is not possible in the turbulent area of the phenomenon, especially in the area where the jump occurs and where its length is measured, so the data must be obtained with direct measurements in a laboratory and through empiric equations. This work presents the results of the generated hydraulic jumps and the measure of its length in a series of tests, where we input different flow rates in a transportable open channel hydraulic with a constant gate opening “ a ” and a slope of S = 0.0035, in the Engineering Faculty Research Centre of the Autonomous University of Chiapas. We also present the experimental method to generate a hydraulic jump, the measure of its length and a comparison with seven empirical equations, including the Sie ñ chi equation used in H-Canales, the most used software for hydraulic channels design in Latin America. The results show that the calculus of L with the proposed equation has a mean squared error (MSE) of 0.1337, a Bias of -0.0049, a model efficiency (ME) of 0.9991 and a determination coefficient ( R 2 ) of 0.9993 when compared with the experimental model. Meanwhile, the comparison of L calculated with the Sie ñ chi equation versus the experimental model resulted in a MSE of 0.1741, a bias of -0.0437, a ME of 0.9984 and a R 2 of 0.9997. Both equations are highly recommended to estimate L in rectangular channels under the conditions presented in this paper, thus, the proposed equation can be applied if y . Finally, it must be stated that we also proved that the Pavlosky equation is comparable in precision and accuracy concerning to proposed equation and Sie ñ chi equation.