Validation of Bagnold’s Approximation of Critical Near-Bed Flow Velocity for Incipient Sediment Motion as Particle Settling Velocity
Publication: Journal of Hydraulic Engineering
Volume 148, Issue 10
Abstract
In the derivation of his bedload formula, Bagnold approximated the critical near-bed flow velocity for incipient sediment motion as the particle settling velocity. However, this approximation has not yet been validated since Bagnold’s bedload formula was proposed in 1973. By comparing the drag coefficient defined based on the critical near-bed flow velocity and that defined based on the particle settling velocity, this note shows that the difference between the two velocities is negligible, which substantiates Bagnold’s approximation.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51979242).
References
Bagnold, R. A. 1973. “The nature of saltation and bed load transport in water.” Proc. R. Soc. London, Ser. A 332 (1591): 473–504. https://doi.org/10.1098/rspa.1973.0038.
Buffington, J. M. 1999. “The legend of A. F. shields.” J. Hydraul. Eng. 125 (4): 376–387. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:4(376).
Buffington, J. M., and D. R. Montgomery. 1997. “A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers.” Water Resour. Res. 33 (8): 1993–2029. https://doi.org/10.1029/96WR03190.
Cheng, N.-S. 1997. “Simplified settling velocity formula for sediment particle.” J. Hydraul. Eng. 123 (2): 149–152. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(149).
Cheng, N.-S. 2008. “Comparison of settling-velocity-based formulas for threshold of sediment motion.” J. Hydraul. Eng. 134 (8): 1136–1141. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:8(1136).
Chien, N., and Z. Wan. 1999. Mechanics of sediment transport. New York: ASCE.
Nikuradse, J. 1933. Stromungsgesetze in rauhen Rohren [Laws of flow in rough pipes]. [In German.] Berlin: VDI Verlag.
Shields, A. 1936. “Anwendung der Aechichkeits-Mechanic und der Turbuleng Forschung auf dir Geschiebewegung’ Mitt Preussische.” In Versuchsanstalt für Wasserbau and Schiffbau. Pasadena, CA: California Institute of Technology.
Yalin, M. S., and E. Karahan. 1979. “Inception of sediment transport.” J. Hydraul. Div. 105 (11): 1433–1443. https://doi.org/10.1061/JYCEAJ.0005306.
Yang, C. T. 1973. “Incipient motion and sediment transport.” J. Hydraul. Div. 99 (10): 1679–1704. https://doi.org/10.1061/JYCEAJ.0003766.
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© 2022 American Society of Civil Engineers.
History
Received: Mar 8, 2022
Accepted: May 27, 2022
Published online: Jul 18, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 18, 2022
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