Simple and General Formula for the Settling Velocity of Particles
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 2
Abstract
A simple, robust, and general formula for the settling velocity of a particle is presented, taking into account the shape and roundness of the particles. It is based on the two asymptotic behaviors of the drag coefficient for low and high Reynolds numbers, respectively. The three coefficients in the proposed equation were fitted for different shape and roundness using explicit relationships. The proposed relationship yields the best results among the studied formulas for many kind of particles with various sizes, shapes, roundnesses, and densities. This formula could therefore be applied to any particle.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by the Japanese Society for the Promotion of Science. The comments from J. Jimenez were greatly appreciated.
References
Ahrens, J. (2000). “A fall-velocity equation.” J. Waterway, Port, Coastal, Ocean Eng., 126(2), 99–102.
Briggs, L., McCulloch, D., and Moser, F. (1962). “The hydraulic shape of sand particles.” J. Sediment. Petrol., 32(4), 645–656.
Chase, R. (1979). “Settling behavior of natural aquatic particulates.” Limnol. Oceanogr., 24(3), 417–426.
Cheng, N.-S. (1997). “Simplified settling velocity formula for sediment particle.” J. Hydraul. Eng., 123(2), 149–152.
Corey, A. (1949). “Influence of the shape on the fall velocity of sand grains.” Master’s thesis, Colorado A&M College, Fort Collins, Colo.
Dallavalle, J. (1948). Micrometrics: The technology of fine particles, Pitman, London.
Dietrich, W. (1982). “Settling velocities of natural particles.” Water Resour. Res., 18(6), 1615–1626.
Engelund, F., and Hansen, E. (1972). A monograph on sediment transport in alluvial streams, Technical Press, Copenhagen, Denmark.
Gibbs, R., Matthews, M., and Link, D. (1971). “The relationship between sphere size and settling velocity.” J. Sediment. Petrol., 41(1), 7–18.
Graf, W. (1971). Hydraulics of sediment transport, McGraw-Hill, New York.
Guo, J. (2002). “Logarithmic matching and its applications in computational hydraulics and sediment transport.” J. Hydraul. Res., 40(5), 555–565.
Hallermeier, R. (1981). “Terminal settling velocity of commonly occurring sand grain.” Sedimentology, 28(6), 859–865.
Hawley, N. (1982). “Settling velocity distribution of natural aggregates.” J. Geophys. Res., C: Oceans Atmos., 87(12), 9489–9498.
Hottovy, J., and Sylvester, D. (1979). “Drag coefficients for irregularly shaped particles.” Ind. Eng. Chem. Process Des. Dev., 18(3), 433–436.
Jimenez, J., and Madsen, O. (2003). “A simple formula to estimate settling velocity of natural sediments.” J. Waterway, Port, Coastal, Ocean Eng., 129(2), 70–78.
Julien, P. (1995). Erosion and sedimentation, Cambridge University Press, Cambridge, U.K.
Komar, P. (1980). “Settling velocity of circular cylinders at low Reynolds numbers.” J. Geol., 88(3), 327–336.
Komar, P., and Reimers, C. (1978). “Grain shape effects on settling rates.” J. Geol., 86(2), 193–209.
Raudkivi, A. (1998). Loose boundary hydraulics, Balkema, Rotterdam, The Netherlands.
Schlichting, H. (1979). Boundary layer theory, McGraw-Hill, New York.
Soulsby, R. (1997). Dynamics of marine sands, a manual for practical applications, Thomas Telford, London.
Stokes, G. (1851). “On the effect of internal friction of fluids on the motion of pendulums.” Trans. Cambridge Philos. Soc., 9, 8–106.
Stringham, G., Simons, D., and Guy, H. (1969). “The behavior of large particles falling in quiescent liquid.” Technical Rep. Professional Paper No. 562-C, U.S. Geological Survey.
Van Rijn, L., Davies, A., Van der Graff, J., and Ribberink, J., eds. (2001). Sedmoc: Sediment transport modelling in marine coastal environments, Aqua, Amsterdam, The Netherlands.
Williams, G. (1966). “Particle roundness and surface texture effects on fall velocity.” J. Sediment. Petrol., 36(1), 255–259.
Wilson, K. (1966). “Bed-load transport at high shear stress.” J. Hydr. Div., 92(11), 49–59.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 2 • February 2007
Pages: 229 - 233
Copyright
© 2007 ASCE.
History
Received: Jun 1, 2005
Accepted: May 16, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.