# Bagnold number

## Description

he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first identified by Ralph Alger Bagnold.

In flows with small Bagnold numbers (Ba < 40), viscous fluid stresses dominate grain collision stresses, and the flow is said to be in the 'macro-viscous’ regime. Grain collision stresses dominate at large Bagnold number (Ba > 450), which is known as the 'grain-inertia’ regime. A transitional regime falls between these two values.

## Variables

Ba | Bagnold number (dimensionless) |

ρ | Particle density (kg/m^{3}) |

d | Grain diameter (m) |

λ | Linear concentration (dimensionless) |

γ | Shear rate ((1/s)) |

μ | Dynamic viscosity of the interstitial fluid (kg/(m*s)) |