# Bagnold Number

Bagnold number, abbreviated as Ba, a dimensionless number, is the ratio of grain collision stresses to various fluid stresses in a granular flow with interstitial Newtonian fluid.

## Bagnold Number formula

\(\large{ Ba = \frac{ \rho \; d^2 \; \lambda^{\frac{1}{2}} \; \dot {\gamma} }{ \mu } }\) |

### Where:

Units |
English |
Metric |

\(\large{ Ba }\) = Bagnold number | \(\large{dimensionless}\) | |

\(\large{ \rho }\) (Greek symbol rho) = density of particle | \(\large{\frac{lbm}{ft^3}}\) | \(\large{\frac{kg}{m^3}}\) |

\(\large{ d }\) = diameter of grain | \(\large{in}\) | \(\large{mm}\) |

\(\large{ \mu }\) (Greek symbol mu) = dynamic viscosity | \(\large{\frac{lbf-sec}{ft^2}}\) | \(\large{ Pa-s }\) |

\(\large{ \lambda }\) (Greek symbol lambda) = linear concentration | \(\large{dimensionless}\) | |

\(\large{ \dot {\gamma} }\) (Greek symbol gamma) = shear rate | \(\large{\frac{lbf}{in^2}}\) | \(\large{ Pa }\) |