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Shields parameter

Dimensionless parameter in fluid mechanics

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Source updated March 21, 2026

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 form of non-dimensionalization of a shear stress, and is typically denoted $\psi$ or $\theta$ . This parameter has been developed by Albert F. Shields, and is called later Shields parameter. The Shields parameter is the main parameter of the Shields formula. The Shields parameter is given by:

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

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.

The critical shear stress and also the critical Shields number ( $\tau _{\ast }$ and $\theta _{\ast }$ ) describe the conditions when the sediment starts moving. Note that the shear stress is a property of the current, while the critical shear stress is a property of the sediment.

01Physical meaning

By multiplying the top and bottom of the Shields parameter by $D^{2}$ , you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.

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Sources and credits

This article is adapted from the Wikipedia article “Shields parameter”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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