Flow Resistance over Mobile Bed in an Open-Channel Flow
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 7
Abstract
This paper deals with the underlying mechanism of flow resistance in an alluvial channel: The effects of sidewall and bed form on flow resistance, Einstein’s divided hydraulic radius approach and Engelund’s energy slope division approach are reexamined. These two approaches assume that the shear stress on a mobile bed is the summation of shear stresses caused by skin friction and bed form. Using a different approach, this paper presents a theoretical relationship between the total bed shear stress with grain and bed-form shear stresses. The contribution of sidewall on the total bed shear stress is also discussed. The writers found that the size of bed form plays a significant role for the flow resistance, and developed relevant expressions for the length of the separation zone behind the bed forms. In addition, a systematical approach has been developed to compute the flow velocity in an alluvial channel. This approach is tested and verified against 5,989 flume and field measurements. The computed and measured discharge/velocity are in good agreement and 83.0% of all data sets fall within the error band.
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Acknowledgments
The writers thank Mr. Chung Cha Fu and Goh Keng Wee, project officers in the Maritime Research Center, Nanyang Technological University, for their assistance in carrying out the data analysis.
References
Bennett, J. P. (1995). “Algorithm for resistance to flow and transport in sand-bed channels,” J. Hydraul. Eng., 121(8), 578–590.
Brownlie, W. R. (1981). “Compilation of fluvial channel data: Laboratory and field.” Rep. No. KH-R43B, W.M. Keck Laboratory of Hydraulics and Water Resources, CIT, Pasadena, Calif.
Cheng, N. S., and Chiew, Y. M. (1998). “Modified logarithmic law for velocity distribution subjected to upward seepage.” J. Hydraul. Eng., 124(12), 1235–1241.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, ASCE, Reston, Va.
Einstein, H. A. (1934). “Der hydaulische oder profil-radius.” Schweizerische Bauzeitung, 103(8), 89–91 (in German).
Einstein, H. A., and Banks, R. B. (1950). “Fluid resistance of composite channels.” Trans., Am. Geophys. Union, 31(4), 603–610.
Einstein, H. A., and Barbarossa, N. L. (1952). “River channel roughness.” Trans. Am. Soc. Civ. Eng., 117, 1121–1146.
Engel, P. (1981). “Length of flow separation over dunes.” J. Hydr. Div., 107(10), 1133–1143.
Engelund, F. (1966). “Hydraulic resistance of alluvial streams.” J. Hydr. Div., 92(2), 315–326.
Engelund, F., and Hansen, E. (1967). A monograph on sediment transport in alluvial streams, Technical University of Denmark Press, Copenhagen, Denmark.
Guy, H. P., Simons, D. B., and Richardson, E. V. (1966). “Summary of alluvial channel data from flume experiments, 1956–61.” Professional Paper No. 462-I, U.S. Geological Survey, Washington, D.C.
Horton, R. E. (1933). “Separate roughness coefficients for channel bottom and sides.” Eng. News-Rec., Nov., 30, 652–653.
Julien, P. Y., and Klaassen, G. J. (1995). “Sand-dune geometry of large rivers during floods.” J. Hydraul. Eng., 121(9), 657–663.
Kalinske, A. A., and Hsia, C. H. (1945). “Study of transportation of fine sediments by flowing water.” Iowa Univ. Studies Eng., Bull., 29, 30.
Karahan, M. Y., and Peterson, A. W. (1980). “Visualization of separation over sand waves.” J. Hydr. Div., 106(8), 1345–1352.
Karim, F. (1995). “Bed configuration and hydraulic resistance in alluvial channel flows.” J. Hydraul. Eng., 121(1), 15–25.
Karim, F. (1999). “Bed-form geometry in sand-bed flows.” J. Hydraul. Eng., 125(12), 1253–1261.
Kennedy, J. F. (1963). “The mechanics of dunes and antidunnes in erodible-bed channels.” J. Fluid Mech., 16(4), 521–544.
Keulegan, C. H. (1938). “Law of turbulent flow in open channels.” J. Res. Natl. Bur. Stand., 21, 707–740.
Meyer-Peter, E. and Muller, R. (1948). “Formulas for bed-load transport.” Proc., 3rd Conf., IAHR, Stockholm, Sweden.
Millar, R. G. (1999). “Grain and form resistance in gravel-bed rivers.” J. Hydraul. Res., 37(3), 303–312.
Neill, C. R. (1967). “Mean velocity criterion for scour of coarse uniform bed-material.” 12th Congress, IAHR, Fort Collins, Colo., 46–54.
Shiono, K., and Knight, D. W. (1991). “Turbulent open-channel flows with variable depth across the channel.” J. Fluid Mech., 222, 617–646.
Smart, G. (1999). “Coefficient of friction for flow resistance in alluvial channels with granular beds.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 136(4), 205–210.
Smith, J. D., and McLean, S. R. (1977). “Spatially averaged flow over a wavy surface.” J. Geophys. Res., 84(12), 1735–1746.
Stein, R. A. (1965). “Laboratory studies of total load and apparent bed load.” J. Geophys. Res., 70(8), 1831–1842.
Tsujimoto, T., Kitamura, T., Fujii, Y., and Nakagawa, H. (1996). “Hydraulic resistance of flow with flexible vegetation in open channel.” J. Hydrosci. Hydr. Eng., 14(1), 47–56.
van Rijn, L. C. (1982). “Equivalent roughness of alluvial bed.” J. Hydr. Div., 108(10), 1215–1218.
van Rijn, L. C. (1984a). “Sediment transport. I: Bed load transport.” J. Hydraul. Eng., 110(10), 1431–1456.
van Rijn, L. C. (1984b). “Sediment transport, Part II: Suspended load transport.” J. Hydraul. Eng., 110(11), 1613–1641.
van Rijn, L. C. (1984c). “Sediment transport. Part III: Bed forms and alluvial roughness.” J. Hydraul. Eng., 110(12), 1733–1754.
Wang, S., and White, W. R. (1993). “Alluvial resistance in transition regime.” J. Hydraul. Eng., 119(6), 725–741.
White, P. J., Paris, E., and Bettess, R. (1981). “The frictional characteristics of alluvial streams: A new approach.” Proc. Inst. Civil Engrg., London, Part 2, 69(3), 737–750.
Williams, P. G. (1970). “Flume width and water depth effects in sediment transport experiments.” Professional Paper No. 562-H, USGS, Washington, D.C.
Yalin, M. S. (1964). “Geometrical properties of sand waves.” J. Hydr. Div., 90(5), 105–119.
Yalin, M. S. (1977). Mechanics of sediment transport, 2nd Ed., Pergmon, New York.
Yang, S. Q. (1993). “The law of boundary shear in rectangular open channels.” J. Sediment Res., 95–103 (in Chinese).
Yang, S. Q. (1996). “Interactions of boundary shear stress, velocity distribution and flow resistance in 3-D open channels.” Ph.D. thesis, Nanyang Technology Univ., Singapore.
Yang, S.-Q., and Lim, S.-Y. (1997). “Mechanism of energy transportation and turbulent flow in a 3-D channel.” J. Hydraul. Eng., 123(8), 684–692.
Yang, S.-Q., and Lim, S.-Y. (1998). “Boundary shear stress distributions in smooth rectangular open channel flows.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 130(3), 163–173.
Yang, S.-Q., and Lim, S.-Y. (2003). “Total Load Transport Formula for Flow in Alluvial Channels.” J. Hydraul. Eng., 129(1), 68–72.
Yang, S.-Q., Tan, S. K., and Lim, S. Y. (2005). “Flow resistance and bed form geometry in a wide alluvial channel.” Water Resour. Res., 41
Yang, S.-Q., Yu, J.-X., and Wang, Y.-Z. (2004). “Estimation of Diffusion Coefficients, Lateral Shear Stress and Velocity in Open Channels with Complex Geometry.” Water Resour. Res., 40(5), 207–217.
Yu, G. L., and Lim, S. Y. (2003). “Modified Manning formula for flow in alluvial channels with sand-beds.” J. Hydraul. Res., 41(6), 597–608.
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Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 7 • July 2008
Pages: 937 - 947
Copyright
© 2008 ASCE.
History
Received: Jun 29, 2004
Accepted: Sep 13, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
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