Shields parameter
# 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 $\theta$. 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. 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 $D^2,$ you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.

