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A Simple Universal Equation for Grain Settling Velocity

¹ Department of Geography, Sheffield University, Sheffield S10 2TN, U.K.; present address: Department of Geography, University of Durham, Durham DH1 3LE, U.K.; r.i.ferguson{at}durham.ac.uk
² Department of Geography, University of British Columbia, Canada

A new equation is presented for sediment fall velocity as a function of grain diameter for given values of fluid viscosity and fluid and solid density. Sediment fall velocity is a fundamental parameter in the modeling and interpretation of fluviatile and coastal deposition. The equation applies to the entire range of viscous to turbulent conditions, and its simple explicit form makes it easy to use in computer models and other applications in sedimentology, geomorphology, and engineering. The equation is derived from dimensional analysis and converges on Stokes' law for small grains and a constant drag coefficient for large grains. Its two physically interpretable parameters are easily adjusted for shape effects or for the use of sieve diameter rather than nominal grain diameter. It gives a close fit to published and new experimental data for both quartz sand and low-density materials, with no more error than previous equations of more complicated form.

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