# Prandtl number

## Description

The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.</p>

Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, the Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.<br />For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents.</p>

Related formulas## Variables

Pr | Prandtl number (dimensionless) (dimensionless) |

ν | momentum diffusivity (kinematic viscosity) (m^2/s) (dimensionless) |

α | thermal diffusivity (m^2/s) (dimensionless) |