Modeling Overfalls Using Vertically Averaged and Moment Equations
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 7
Abstract
A new set of vertically averaged and moment equations, which assumes a linear longitudinal velocity distribution and quadratic vertical velocity and pressure distributions, is used for modeling flow in the vicinity of horizontal rectangular free overfall with smooth and rough beds and sharp-crested weirs with sloping upstream faces. These equations are modeled using a hybrid Petrov-Galerkin and Bubnov-Galerkin finite-element scheme. For the rectangular free overfalls, the predicted water surface profiles upstream of the overfall and the free jet trajectory agree well with the measured data. The computed vertical velocity and pressure distributions at the brink and upstream of the overfall are found to be in good agreement with the measured data; while the computed longitudinal velocity distributions compare well with a two-dimensional potential flow model. The computed results for sharp-crested weirs with sloping upstream faces agree well with the measured data for an upstream weir slope of up to 27° with the horizontal. For an upstream slope of 45° and steeper and for a large weir height the predicted water surface upstream of a weir shows numerical instability.
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References
1.
Ali, K. H. M., and Sykes, A.(1972). “Free-vortex theory applied to free overfall.”J. Hydr. Div., ASCE, 98(5), 973–979.
2.
Bureau of Reclamation. (1948). “Studies of crests for free overfall dams.”Boulder Canyon Proj. Final Rep., Part VI-Hydr. Investigations, Bull. 3.
3.
Clarke, N. S. (1965). “On two-dimensional inviscid flow in a waterfall.”J. Fluid Mech., Vol. 22, Part 2, 359–369.
4.
Hager, W. H.(1982). “Hydraulics of plane free overfall.”J. Hydr. Engrg., ASCE, 109(12), 1683–1697.
5.
Hicks, F. E., and Steffler, P. M.(1992). “Characteristic dissipative Galerkin scheme for open-channel flow.”J. Hydr. Engrg., ASCE, 118(2), 337–352.
6.
Khan, A. A., and Steffler, P. M.(1996). “Vertically averaged and moment equations model for flow over curved beds.”J. Hydr. Engrg., ASCE, 122(1), 3–9.
7.
Marchi, E.(1993). “On the free overfall.”J. Hydr. Res., 31(6), 777–790.
8.
Markland, E. (1965). “Calculation of flow at a free overfall by relaxation method.”Proc., Inst. of Civ. Engrs., London, England, Vol. 31, 71–78.
9.
Montes, J. S. (1992). “A potential flow solution for the free overfall.”Proc., Inst. of Civ. Engrs., Water, Maritime and Energy, Vol. 96, 259–266.
10.
Paderi, F. (1954). “Sulla Chiamata di Sbocco.”L'Energia Elettrica, 742–748.
11.
Paderi, F. (1956). “Sulla Chiamata di Sbocco in Canale a Fondo Declive.”L'Energia Elettrica, 792–800.
12.
Paderi, F. (1959). “Sulla Chiamata di Sbocco in Canale a Fondo Acclive.”L'Energia Elettrica, 883–888.
13.
Rajaratnam, N., and Muralidhar, D.(1968). “Characteristics of the rectangular free overfall.”J. Hydr. Res., 6(3), 233–258.
14.
Rajaratnam, N., Muralidhar, D., and Beltaos, S.(1976). “Roughness effects on rectangular free overfall.”J. Hydr. Div., 102(5), 599–614.
15.
Rouse, H.(1936). “Discharge characteristics of the free overfall.”Civ. Engrg., 6(4), 257–260.
16.
Rouse, H. (1943). “Discussion to energy loss at the base of free overfall.”Trans., ASCE, New York, N.Y., Vol. 108, 1383–1387.
17.
Steffler, P. M., and Jin, Y.(1993). “Depth averaged and moment equations for moderately shallow free surface flow.”J. Hydr. Res., 31(1), 5–17.
18.
Strelkoff, T., and Moayeri, M. S.(1970). “Pattern of potential flow in a free overfall.”J. Hydr. Div., ASCE, 96(4), 879–901.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Jul 1, 1996
Published in print: Jul 1996
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