Shields parameter

The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow. It is a nondimensionalization of a shear stress, and is typically denoted $\tau _{\ast }$ or $\theta$ . It is given by:

\tau _{\ast }=\theta ={\frac {\tau }{(\rho _{s}-\rho )gD}},

where:

$\tau$ is a dimensional shear stress;
$\rho_s$ is the density of the sediment;
$\rho$ is the density of the fluid;
$g$ is acceleration due to gravity;
$D$ is a characteristic particle diameter of the sediment.

Physical meaning

By multiplying the top and bottom of the Shields parameter by D², you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.

References

Shields, A. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung [Application of similarity mechanics and turbulence research on shear flow] (PDF). Mitteilungen der Preußischen Versuchsanstalt für Wasserbau (in German). 26. Berlin: Preußische Versuchsanstalt für Wasserbau.
Shields, A. (1936). Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung [Application of similarity principles and turbulence research to bed-load movement] (PDF). Mitteilungen der Preußischen Versuchsanstalt für Wasserbau. 26. Berlin: Preußische Versuchsanstalt für Wasserbau.

External links

Southard, John. "Chapter 9 – Threshold of movement" (PDF). Lecture notes – Special topics: An introduction to fluid motions, sediment transport, and current-generated sedimentary structures. MIT Open Courseware. Retrieved 2011-01-31.

Dimensionless numbers in fluid mechanics

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