# Shields Parameter

## Description

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.

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.

## Variables

τ_{asterisk} | Shields parameter (dimensionless) |

τ | dimensional shear stress (pascal) |

ρ_{s} | density of the sediment (kg/m^{3}) |

ρ | density of the fluid (kg/m^{3}) |

g | Standard gravity |

D | characteristic particle diameter of the sediment (m) |