A Study of an Empirical Sequent Depths Equation of the Hydraulic Jump in a Horizontal Trapezoidal Channel

Authors

  • Nguyen Minh Ngoc Faculty of Urban Environmental and Infrastructural Engineering, Hanoi Architectural University, Vietnam https://orcid.org/0000-0002-2664-5558
  • Tran Ngoc Thang Hanoi University of Business and Technology, Vietnam
Volume: 13 | Issue: 6 | Pages: 12307-12313 | December 2023 | https://doi.org/10.48084/etasr.6431

Abstract

This study used existing studies and incorporated Pi theory to establish the connection between the sequent depth ratio (y2/y1) and the influencing factors (Fr1 and M1) on the hydraulic jump on a smooth horizontal trapezoidal channel, using a physical model with a side slope of 1:1. The study proposed four equations, from which the empirical equation (Y3) was used to calculate the y2/y1 ratio of the steady jump (4.0 ≤ Fr1 ≤ 9.0). An analysis of statistical indicators for (Y3) showed that the maximum error was 7.4%, R2 was 0.98, and other statistical indicators were close to the ideal point at zero (MSE = 0.027, RMSE = 0.163, MEA = 0.129, and MAPE ≈ 2.2%). Furthermore, statistical analysis for test data also provided good results (R2 = 0.94, MSE = 0.107, RMSE = 0.327, MEA = 0.25, and MAPE ≈ 3.7%), and the maximum error reached 8.8%. Therefore, the proposed equation ensures that the calculated values can be used in practice.

Keywords:

sequent depth, trapezoidal channel, empirical equation, Bélanger, hydraulic jump

Downloads

Download data is not yet available.

References

S. Montes, Hydraulics of open channel flow. Baltimore, MD, USA: American Society of Civil Engineers, 1998.

A. S. Kote and P. B. Nangare, "Hydraulic Model Investigation on Stepped Spillway’s Plain and Slotted Roller Bucket," Engineering, Technology & Applied Science Research, vol. 9, no. 4, pp. 4419–4422, Aug. 2019.

S. M. Kori, A. A. Mahessar, M. Channa, A. A. Memon, and A. R. Kori, "Study of Flow Characteristics Over a Rounded Edge Drop Structure in Open Channel," Engineering, Technology & Applied Science Research, vol. 9, no. 3, pp. 4136–4139, Jun. 2019.

N. P. Mahmoud and A. Zabihi, "Numerical Simulation of a Single-Phase Flow Through Fractures with Permeable, Porous and Non-Ductile Walls," Engineering, Technology & Applied Science Research, vol. 7, no. 5, pp. 2041–2046, Oct. 2017.

H. T. An, Hydraulic Construction. Hanoi, Vietnam: Agricultural Publishing House, 2012.

V. T. Chow, Open Channel Hydraulics. New York, NY, USA: McGraw Hill, 1958.

N. Rajaratnam, "The Hydraulic Jump in Sloping Channels," Irrigation va Power, vol. 23, no. 2, pp. 137–149, 1966.

K. V. N. Sarma and D. A. Newnham, "Surface Profiles of Hydraulic Jump for Froude Numbers less than Four," Water Power, vol. 25, no. 4, pp. 139–142, Apr. 1973.

S. A. Ead and N. Rajaratnam, "Hydraulic Jumps on Corrugated Beds," Journal of Hydraulic Engineering, vol. 128, no. 7, pp. 656–663, Jul. 2002.

R. Wanoschek and W. H. Hager, "Hydraulic jump in trapezoidal channel," Journal of Hydraulic Research, vol. 27, no. 3, pp. 429–446, May 1989.

S. S. Muhsun, "Characteristics of the Hydraulic Jump in Trapezoidal Channel Section," Journal of Environmental Studies, vol. 9, no. 1, pp. 53–63, Dec. 2012.

K. Samir, "Etude Theorique et Experimentale de Quelques Types de Ressauts Hydrauliques Dans un Canal Trapezoidal," Ph.D. dissertation, University of Biskra, Algeria, 2014.

S. kateb, M. Debabeche, and F. Riguet, "Hydraulic Jump in a Sloped Trapezoidal Channel," Energy Procedia, vol. 74, pp. 251–257, Aug. 2015.

S. Cherhabil and M. Debabeche, "Experimental Study of Sequent Depths Ratio of Hydraulic Jump in Sloped Trapezoidal Chanel," International Symposium on Hydraulic Structures, pp. 353–358, Jun. 2016.

R. Siad, "Ressaut hydraulique dans un canal trapézoïdal brusquement élargi," Ph.D. dissertation, University of Biskra, Algeria, 2018.

S. A. Shanin, K. M. Othman, and A. G. Alan, "Experimental Study of Hydraulic Jump Characteristics in Trapezoidal Channels," ZANCO Journal of Pure and Applied Sciences, vol. 30, no. s1, pp. 70–75, 2018.

B. Fatehi Nobarian, H. Hajikandi, Y. Hassanzadeh, and S. Jamali, "Investigación experimental y analítica de los efectos de las células secundarias actuales en las características del salto hidráulico en canales trapezoidales," Tecnología y Ciencias del Agua, vol. 10, no. 3, pp. 190–218, May 2019.

W. H. Hager, Energy Dissipators and Hydraulic Jump. Dordrecht, Netherlands: Springer Science & Business Media, 2013.

H. E. Schulz et al., "Details of Hydraulic Jumps for Design Criteria of Hydraulic Structures," in Hydrodynamics - Concepts and Experiments, London, UK: IntechOpen, 2015.

M. A. R. Eltoukhy, "Hydraulic Jump Characteristics for Different Open Channel and Stilling Basin Layouts," International Journal of Civil Engineering and Technology, vol. 7, no. 2, pp. 290–301, Mar. 2016.

A. Alikhani, R. Behrozi-Rad, and M. Fathi-Moghadam, "Hydraulic jump in stilling basin with vertical end sill," International Journal of Physical Sciences, vol. 5, no. 1, pp. 25–29, Jan. 2010.

J. A. Mccorquodale and M. S. Mohamed, "Hydraulic jumps on adverse slopes," Journal of Hydraulic Research, vol. 32, no. 1, pp. 119–130, Jan. 1994.

A. J. Peterka, Hydraulic Design of Stilling Basins and Energy Dissipators. Department of the Interior, Bureau of Reclamation, 1978.

S. Pagliara and M. Palermo, "Hydraulic jumps on rough and smooth beds: aggregate approach for horizontal and adverse-sloped beds," Journal of Hydraulic Research, vol. 53, no. 2, pp. 243–252, Mar. 2015.

F. G. Carollo, V. Ferro, and V. Pampalone, "New Solution of Classical Hydraulic Jump," Journal of Hydraulic Engineering, vol. 135, no. 6, pp. 527–531, Jun. 2009.

F. G. Carollo, V. Ferro, and V. Pampalone, "Sequent Depth Ratio of a B-Jump," Journal of Hydraulic Engineering, vol. 137, no. 6, pp. 651–658, Jun. 2011.

I. Ohtsu and Y. Yasuda, "Hydraulic Jump in Sloping Channels," Journal of Hydraulic Engineering, vol. 117, no. 7, pp. 905–921, Jul. 1991.

N. M. Ngoc, P. H. Cuong, T. T. Son, N. V. Nam, and N. T. Phong, "Experimental study of the hydraulic jump length in a smooth trapezoidal channel," Przegląd Naukowy Inżynieria i Kształtowanie Środowiska, vol. 31, no. 1, pp. 63–76, 2022.

N. M. Ngoc, P. H. Cuong, and B. H. P. Phong, "Prediction of the conjugate depth of the hydraulic jump in the trapezoidal channel using Random Forest regression," Journal of Military Science and Technology, no. 82, pp. 150–158, Oct. 2022.

F. Yousefi, J. Mozaffari, and S. a. M. Movahed, "Developing a hydraulic jump length model on horizontal rough beds," Journal of the South African Institution of Civil Engineering, vol. 61, no. 3, pp. 2–6, Sep. 2019.

M. Palermo and S. Pagliara, "A review of hydraulic jump properties on both smooth and rough beds in sloping and adverse channels.," Acta Scientiarum Polonorum - Formatio Circumiectus, vol. 16, no. 1, pp. 91–105, 2017.

W. H. Hager and R. Bremen, "Classical hydraulic jump: sequent depths," Journal of Hydraulic Research, vol. 27, no. 5, pp. 565–585, Sep. 1989.

D. S. Moore, W. I. Notz, and M. A. Fligner, The Basic Practice of Statistics, Ninth edition. Austin, TX, USA: W. H. Freeman, 2021.

S. Boubaker, "A Predictive Vaccination Strategy Based on a Swarm Intelligence Technique for the Case of Saudi Arabia: A Control Engineering Approach," Engineering, Technology & Applied Science Research, vol. 13, no. 4, pp. 11091–11095, Aug. 2023.

C. J. Willmott and K. Matsuura, "Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance," Climate Research, vol. 30, no. 1, pp. 79–82, Dec. 2005.

Downloads

How to Cite

[1]
N. M. Ngoc and T. N. Thang, “A Study of an Empirical Sequent Depths Equation of the Hydraulic Jump in a Horizontal Trapezoidal Channel”, Eng. Technol. Appl. Sci. Res., vol. 13, no. 6, pp. 12307–12313, Dec. 2023.

Metrics

Abstract Views: 256
PDF Downloads: 256

Metrics Information