Back
 JWARP  Vol.11 No.12 , December 2019
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 Sieñchi 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 (R2) of 0.9993 when compared with the experimental model. Meanwhile, the comparison of L calculated with the Sieñchi equation versus the experimental model resulted in a MSE of 0.1741, a bias of -0.0437, a ME of 0.9984 and a R2 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 Sieñchi equation.
Cite this paper: Mundo-Molina, M. and Pérez, J. (2019) 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. Journal of Water Resource and Protection, 11, 1481-1488. doi: 10.4236/jwarp.2019.1112086.
References

[1]   Levi, L.E. (2001) El agua según la ciencia. Asociación Mexicana de Hidráulica. Instituto Mexicano de Tecnología del Agua. Jiutepec, Morelos, México.

[2]   Ewah, E.G., Nyah, E.E., Antigha, R.A. and Egbe, J.G. (2018) Experimental Investigation of Energy Dissipation in Hydraulic Jump: A Comparison of Weir and Level Bedded Constricted Flume. International Journal of Engineering Trends and Technology, 61, 6-13.

[3]   Youngkyu, K., Gyewoon, C., Hyoseon, P. and Seongjoon, B. (2015) Hydraulic Jump and Energy Dissipation with Sluice Gate. Water, 7, 5115-5133.
https://doi.org/10.3390/w7095115

[4]   Kumar, G.S., Mehta, R.C. and Dwivedi, V.K. (2013) Modeling of Relative Length and Relative Energy Loss of Free Hydraulic Jump in Horizontal Prismatic Channel. Procedia Engineering, 51, 529-537.
https://doi.org/10.1016/j.proeng.2013.01.075

[5]   Bélanger, J.B. (1849) Notes sur le cours dhydraulique Notes on a course in hydraulics. Mém. EcoleNat. Ponts et Chaussées, Paris, France, 1849-1850.

[6]   Bakhmeteff, B.A. (1932) Hydraulics of Open Channels. McGraw-Hill, New York.

[7]   Bradley, J.N. and Peterka, A.J. (1957) The Hydraulic Design of Stilling Basins: Stilling Basin with Sloping Apron (Basin V). Journal of the Hydraulics Division, 83, 1-32.

[8]   Chow, V.T. (1959) Open-Channel Hydraulics. McGraw-Hill, New York.

[9]   Henderson, F.M. (1966) Open Channel Flow. MacMillan, New York.

[10]   Herbrand, K. (1973) The Spatial Hydraulic Jump. Journal of Hydraulic Research, 11, 205-218.
https://doi.org/10.1080/00221687309499774

[11]   Bhutto, H.B.G. (1987) Hydraulic Jump Control and Energy Dissipation. PhD Thesis, Mehran University of Engineering & Technology, Jamshoro.

[12]   Hager, W.H. (1992) Energy Dissipators & Hydraulic Jumps. Kluwer Academic Publication, Dordrecht, The Netherlands, 151-173.
https://doi.org/10.1007/978-94-015-8048-9

[13]   Rajaratnam, N. and MacDougall, R.K. (1983) Erosion by Plane Wall Jets with Minimum Tail Water. Journal of Hydraulic Engineering, 109, 1061-1064.
https://doi.org/10.1061/(ASCE)0733-9429(1983)109:7(1061)

[14]   Gardea, V.H. (1999) Hidráulica de canales. Facultad de Ingeniería, UNAM. México, D.F.

[15]   Sotelo, A.G. (2002) Hidráulica de canales. Facultad de Ingeniería de la Universidad Nacional Autónoma de México. Ciudad de México, México.

[16]   Chanson, H. (2006) Minimum Specific Energy and Critical Flow Conditions in Open Channels. Journal of Irrigation and Drainage Engineering, 132, 498-502.
https://doi.org/10.1061/(ASCE)0733-9437(2006)132:5(498)

[17]   Chow, V.T. (2004) Hidráulica de canales abiertos. McGraw-Hill, Bogotá, Colombia.

[18]   Vatankhah, R.A. and Valiani, A. (2011) Analytical Inversion of Specific Energy Depth Relationship in Channels with Parabolic Cross Sections. Journal des Sciences Hydrologiques, 56, 834-840.
https://doi.org/10.1080/02626667.2011.583250

[19]   Mundo, M.M. (2014) Diseno y construcción de una canal económico en el laboratorio de hidráulica de la Facultad de Ingeniería de la UNACH. Congreso Latinoamericano de Hidráulica, Santiago de Chile.

[20]   Mundo, M.M. (2018) Volumetric Measuring of Sediment in a Transportable Prismatic Channel. Revista Internacional de contaminación Ambiental, 34, 173-176.

[21]   Villón, B.M. (2016) H-Canales 3.1. Manual de usuario. Lima, Perú.

 
 
Top