Numerical Modeling of Free Overfall
Publication: Journal of Hydraulic Engineering
Volume 131, Issue 2
Abstract
Free overfall is treated by using two-dimensional steady potential flow theory. Based on the theory of the boundary value problem of analytical function and the substitution of variables we derive the boundary integral equations in the physical plane for solving the free overfall in a rectangular channel. A numerical iterative method has been developed to solve these boundary integral equations. The free water surface profiles, pressure distribution, and the end-depth ratio are calculated for a wide range of bed slopes, bed roughness, and incoming upstream Froude number. The computed results agree well with the available experimental data.
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Acknowledgments
The writer wishes to thank two anonymous reviewers and the Associate Editor for their helpful comments of this paper.
References
Cheng, A. H-D., Liggett, J. A., and Liu, P. L-F. (1981). “Boundary calculations of sluice and spillway flows.” J. Hydraul. Div., Am. Soc. Civ. Eng., 107(10), 1163–1178.
Clarke, N. S. (1965). “On the two-dimensional inviscid flow in a waterfall.” J. Fluid Mech., 22(II), 359–369.
Davis, A. C., Ellett, B. G.S., and Jacob, R. P. (1998). “Flow measurement in sloping channels with rectangular free overfall.” J. Hydraul. Eng., 124(7), 760–763.
Delleur, J. W., Dooge, J. C., and Gent, K. W. (1956). “Influence of slope and roughness on the free overfall.” J. Hydraul. Div., Am. Soc. Civ. Eng., 82(4), 1–35.
Diersch, H. J., Schirmer, A., and Busch, K. F. (1977). “Analysis of flows with initially unknown discharge.” J. Hydraul. Div., Am. Soc. Civ. Eng., 103(3), 213–232.
Guo, Y. K., Wen, X., and Wu, C. G. (1996). “Flow through slit in dam.” J. Hydraul. Eng., 122(11), 662–669.
Guo, Y. K., Wen, X., Wu, C. G., and Fang, D. (1998). “Numerical modelling of spillway flow with free drop and initially unknown discharge.” J. Hydraul. Res., 36(5), 785–801.
Hager, W. H. (1983). “Hydraulics of plane free overfall.” J. Hydraul. Eng., 109(12), 1683–1697.
Khan, A. A., and Steffler, P. M. (1996). “Modeling overfalls using vertically averaged and momentum equations.” J. Hydraul. Eng., 122(7), 397–402.
Marchi, E. (1993). “On the free overfall.” J. Hydraul. Res., 31(6), 777–790.
Montes, J. S. (1992). “A potential flow solution for the free overfall.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 96, 259–266.
Muskhelishvili, N. I. (1966). Singular integral equations, Shanghai Science and Technology Press, Shanghai, China (in Chinese, translated from Russian).
Rajaratnam, N., and Muralidhar, D. (1968). “Characteristics of the rectangular free overfall.” J. Hydraul. Res., 6(3), 233–258.
Rajaratnam, N., Muralidhar, D., and Beltaos S. (1976). “Roughness effects on rectangular free overfall.” J. Hydraul. Div., Am. Soc. Civ. Eng., 102(5), 599–614.
Rouse, H. (1936). “Discharge characteristics of the free overfall.” Civ. Eng. (N.Y.), 6(4), 257–260.
Southwell, R., and Vaisey, G. (1946). “Relaxation methods applied to engineering problems. XII. Fluid motions characterized by ‘free’ streamline.” Philos. Trans. R. Soc. London, Ser. A, 240, 117–161.
Strelkoff, T. S., and Moayeri, M. S. (1970). “Pattern of potential flow in a free overfall.” J. Hydraul. Div., Am. Soc. Civ. Eng., 96(4), 879–901.
Vanden-Broeck, J.-M. (1997). “Numerical calculation of the free-surface flow under a sluice gate.” J. Fluid Mech., 330, 339–347.
White, F. M. (1986). Fluid mechanics, 2nd Ed., McGraw-Hill, New York.
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Published In
Journal of Hydraulic Engineering
Volume 131 • Issue 2 • February 2005
Pages: 134 - 138
Copyright
© 2005 ASCE.
History
Received: Mar 3, 2003
Accepted: Jun 15, 2004
Published online: Feb 1, 2005
Published in print: Feb 2005
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