Average Velocity of Solitary Coarse Grain in Flows over Smooth and Rough Beds
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 6
Abstract
A formula is derived for the prediction of the average velocity of a solitary coarse grain moving over a rigid flat channel bed. To verify the theoretical consideration, data collected in the present study and reported in the literature (811 sets in total) are analyzed for typical bed roughness configurations. The results show significant improvements in the prediction of solitary grain velocity for both smooth- and rough-bed conditions in comparison with other formulas available in the literature. From the proposed formula, it follows that for rough-bed conditions, the dimensionless grain velocity depends on the Shields number and also the ratio of bed-roughness height to the grain diameter. The present study is limited to motion of solitary grains, but the result obtained implies that bed-load transport rate could be also affected by the equivalent bed-roughness height even under mobile bed conditions and such effects may become pronounced for nonuniform sediments.
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Acknowledgments
This study was partially supported by the Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, P. R. China.
References
Abbott, J. E., and Francis, J. R. D. (1977). “Saltation and suspension trajectories of solid grains in a water stream.” Philos. Trans. R. Soc. Math. Phys. Eng. Sci., 284(1321), 225–254.
Bagnold, R. A. (1973). “The nature of saltation and of ‘bed-load’ transport in water.” Proc. R. Soc. London A, 332(1591), 473–504.
Bathurst, J. C., Li, R. M., and Simons, D. B. (1981). “Resistance equation for large-scale roughness.” J. Hydraul. Div., 107(12), 1593–1613.
Bounvilay, B. (2003). “Transport velocities of bedload particles in rough open channel flows.” Ph.D. thesis, Colorado State Univ.
Bridge, J. S., and Dominic, D. F. (1984). “Bed-load grain velocities and sediment transport rates.” Water Resour. Res., 20(4), 476–490.
Buffington, J. M., Dietrich, W. E., and Kirchner, J. W. (1992). “Friction angle measurements on a naturally formed gravel streambed—implications for critical boundary shear-stress.” Water Resour. Res., 28(2), 411–425.
Cheng, N. S. (1997). “Simplified settling velocity formula for sediment particle.” J. Hydraul. Eng., 149–152.
Cheng, N. S. (2002). “Exponential formula for bedload transport.” J. Hydraul. Eng., 942–946.
Cheng, N. S. (2008). “Comparison of settling-velocity-based formulas for threshold of sediment motion.” J. Hydraul. Eng., 1136–1141.
Cheng, N. S. (2009). “Comparison of formulas for drag coefficient and settling velocity of spherical particles.” Powder Technol., 189(3), 395–398.
Cheng, N. S., Nguyen, H. T., Zhao, K. F., and Tang, X. N. (2011). “Evaluation of flow resistance in smooth rectangular open channels with modified prandtl friction law.” J. Hydraul. Eng., 441–450.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, ASCE, Reston, VA.
Einstein, H. A. (1950). “The bed-load function for sediment transportation in open channel flows.” U.S. Dept. of Agriculture, Washington, DC.
Ferguson, R. (2007). “Flow resistance equations for gravel- and boulder-bed streams.” Water Resour. Res., 43(5), W05427.
Fernandez Luque, R. (1974). “Erosion and transport of bed-load sediment.” Ph.D. thesis, Delft Univ. of Technology, Netherlands.
Fernandez Luque, R., and van Beek, R. (1976). “Erosion and transport of bed-load sediment.” J. Hydraul. Res., 14(2), 127–144.
Francis, J. R. D. (1973). “Experiments on the motion of solitary grains along the bed of a water-stream.” Proc. R. Soc. London, Ser. A, 332(1591), 443–471.
Fredsoe, J., and Deigaard, R. (1992). Mechanics of coastal sediment transport, World Scientific, Singapore.
Hu, C. H., and Hui, Y. J. (1996). “Bed-load transport. 1. Mechanical characteristics.” J. Hydraul. Eng., 245–254.
Johnston, C. E., Andrews, E. D., and Pitlick, J. (1998). “In situ determination of particle friction angles of fluvial gravels.” Water Resour. Res., 34(8), 2017–2030.
Julien, P. Y., and Bounvilay, B. (2013). “Velocity of rolling bed load particles.” J. Hydraul. Eng., 177–186.
Laursen, E. M. (1999). “Pickup probability for sediment entrainment—Discussion.” J. Hydraul. Eng., 786–787.
Lavelle, J. W., and Mofjeld, H. O. (1987). “Do critical stresses for incipient motion and erosion really exist.” J. Hydraul. Eng., 370–385.
Lee, H. Y., Chen, Y. H., You, J. Y., and Lin, Y. T. (2000). “Investigations of continuous bed load saltating process.” J. Hydraul. Eng., 691–700.
Lee, H. Y., and Hsu, I. S. (1994). “Investigation of saltating particle motions.” J. Hydraul. Eng., 831–845.
Miller, R., and Byrne, R. J. (1966). “The angle of repose for a single grain on a fixed rough bed.” Sedimentology, 6(4), 303–314.
Nakagawa, H., and Tsujimoto, T. (1981). “Hydrodynamic drag force acting upon a spherical particle on a rough bed composed of identical particles.” Bull. Disast. Prev. Res. Inst., 31(2), 115–130.
Niño, Y., and García, M. (1998). “Experiments on saltation of sand in water.” J. Hydraul. Eng., 1014–1025.
Niño, Y., García, M., and Ayala, L. (1994). “Gravel saltation. 1. Experiments.” Water Resour. Res., 30(6), 1907–1914.
Paintal, A. S. (1971). “A stochastic model of bed load transport.” J. Hydraul. Res., 9(4), 527–554.
Parsons, D. A. (1972). “The speeds of sand grains in laminar flow over a smooth bed.” Sedimentation: Symp. to Honor Prof. H. A. Einstein, H. W. Shen, ed., Colorado State Univ., Fort Collins, CO.
Ranga Raju, K. G., Asawa, G. L., and Mishra, H. K. (2000). “Flow-establishment length in rectangular channels and ducts.” J. Hydraul. Eng., 533–539.
Recking, A., Frey, P., Paquier, A., Belleudy, P., and Champagne, J. Y. (2008). “Bed-load transport flume experiments on steep slopes.” J. Hydraul. Eng., 1302–1310.
Schmeeckle, M. W., Nelson, J. M., and Shreve, R. L. (2007). “Forces on stationary particles in near-bed turbulent flows.” J. Geophys. Res. Earth Surf., 112(F02003), 1–21.
van Rijn, L. C. (1982). “Equivalent roughness of alluvial bed.” J. Hydraul. Div., 1215–1218.
van Rijn, L. C. (1984). “Sediment transport. 1. Bed-load transport.” J. Hydraul. Eng., 1431–1456.
Whitehouse, R. J. S., Soulsby, R. L., and Damgaard, J. S. (2000). “Inception of sediment transport on steep slopes—Discussion.” J. Hydraul. Eng., 553–555.
Wiberg, P. L., and Smith, J. D. (1987). “Calculations of the critical shear-stress for motion of uniform and heterogeneous sediments.” Water Resour. Res., 23(8), 1471–1480.
Wu, W. (2008). Computational river dynamics, Vol. XIII, Taylor & Francis, London.
Wu, W., Altinakar, M., and Wang, S. S. Y. (2006). “Depth average analysis of hysteresis between flow and sediment transport under unsteady conditions.” Int. J. Sediment Res., 21(2), 101–112.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 6 • June 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 3, 2013
Accepted: Jan 23, 2014
Published online: Feb 26, 2014
Published in print: Jun 1, 2014
Discussion open until: Jul 26, 2014
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