# Archimedes number

## Description

In viscous fluid dynamics, the Archimedes number (Ar) (not to be confused with Archimedes’ constant, π), named after the ancient Greek scientist Archimedes is used to determine the motion of fluids due to density differences. It is a dimensionless number defined as the ratio of external forces to internal viscous forces and has the form shown here.

Related formulas## Variables

Ar | Archimedes number (dimensionless) |

g | local external field (for example gravitational acceleration) (m/s^{2}) |

L | characteristic length of body (m) |

ρ_{l} | density of the fluid (kg/m^{3}) |

ρ | density of the body (kg/m^{3}) |

μ | dynamic viscosity (kg/m*s) |