# Air - Prandtl Number

## Figures and table showing changes in Prandtl number for air with changes in temperature and pressure

**The Prandtl Number** - Pr - is a *dimensionless number* approximating the ratio of *momentum diffusivity* (kinematic viscosity) to *thermal diffusivity* - and is often used in heat transfer and free and forced convection calculations.

The Prandtl number can for calculations be expressed as

Pr = μ c

_{p}/ k (1)where

μ = absolute or dynamic viscosity [kg/(m s)], [lb_{m}/(ft h)]

c_{p}= specific heat [J/(kg K)], [Btu/(lb_{m }^{o}F)]

k = thermal conductivity [W/(m K)], [Btu/(h ft^{2 }^{o}F/ft)]

Below, Prandtl numbers for air at varying temperatures and pressures are given in figures and tables.

See also other properties of** Air **at **varying temperature and pressure: **Density and specific weight at varying temperature, Density at varying pressure, Diffusion Coefficients for Gases in Air, Specific heat at varying temperature and Specific heat at varying pressure, Thermal Conductivity, Thermal Diffusivity, Properties at gas-liquid equilibrium conditions and Air thermophysical properties at standard conditions and Composition and molecular weight,

as well as **Prandtl number** of Ammonia, Carbon dioxide, Methane, Nitrogen, Propane and Water.

Air Prandtl number at 1 bara pressure, temperature given as °C or °F:

Air Prandtl number at varying temperatures and constant pressures, SI and Imperial units:

Air Prandtl number at 1 bara pressure, temperature given as °C or °F:

Temperature | Pr | Temperature | Pr |

[°C] | [-] | [°F] | [-] |

-100 | 0.734 | -150 | 0.733 |

-50 | 0.720 | -50 | 0.719 |

0 | 0.711 | 0 | 0.714 |

25 | 0.707 | 60 | 0.709 |

50 | 0.705 | 75 | 0.708 |

100 | 0.701 | 100 | 0.706 |

150 | 0.699 | 200 | 0.701 |

200 | 0.698 | 300 | 0.699 |

250 | 0.699 | 400 | 0.698 |

300 | 0.702 | 500 | 0.700 |

Air Prandtl number at given temperatures and 1, 5 10 and 20 bara pressure:

Temperature | Prandtl number at given pressures | |||||

[K] | [°C] | [°F] | 1 bara,14.5 psia | 5 bara,72.5 psia | 10 bara, 145 psia | 20 bara,725 psia |

60 | -213.2 | -351.7 | 4.138 | 4.153 | 4.170 | 4.187 |

80 | -193.2 | -315.7 | 1.7 | 2.252 | 2.259 | 2.269 |

100 | -173.2 | -279.7 | 0.780 | 0.898 | 1.783 | 1.770 |

120 | -153.2 | -243.7 | 0.759 | 0.806 | 0.890 | 1.360 |

140 | -133.2 | -207.7 | 0.747 | 0.773 | 0.812 | 0.923 |

180 | -93.2 | -135.7 | 0.731 | 0.743 | 0.759 | 0.792 |

200 | -73.2 | -99.7 | 0.726 | 0.735 | 0.745 | 0.769 |

220 | -53.2 | -63.7 | 0.721 | 0.728 | 0.736 | 0.754 |

240 | -33.2 | -27.7 | 0.717 | 0.722 | 0.729 | 0.742 |

260 | -13.2 | 8.3 | 0.713 | 0.718 | 0.723 | 0.734 |

273 | 0.0 | 32.0 | 0.711 | 0.715 | 0.720 | 0.729 |

280 | 6.9 | 44.3 | 0.710 | 0.714 | 0.718 | 0.727 |

289 | 15.6 | 60.0 | 0.709 | 0.713 | 0.716 | 0.723 |

300 | 26.9 | 80.3 | 0.707 | 0.711 | 0.714 | 0.722 |

320 | 46.9 | 116.3 | 0.705 | 0.708 | 0.711 | 0.717 |

340 | 66.9 | 152.3 | 0.703 | 0.705 | 0.708 | 0.714 |

360 | 86.9 | 188.3 | 0.701 | 0.703 | 0.706 | 0.711 |

380 | 106.9 | 224.3 | 0.700 | 0.702 | 0.704 | 0.709 |

400 | 126.9 | 260.3 | 0.699 | 0.701 | 0.703 | 0.706 |

500 | 226.9 | 440.3 | 0.698 | 0.700 | 0.701 | 0.703 |

600 | 326.9 | 620.3 | 0.703 | 0.704 | 0.704 | 0.706 |

700 | 426.9 | 800.3 | 0.710 | 0.710 | 0.711 | 0.712 |

800 | 526.9 | 980.3 | 0.717 | 0.718 | 0.718 | 0.719 |

900 | 626.9 | 1160.3 | 0.724 | 0.725 | 0.725 | 0.725 |

1000 | 726.9 | 1340.3 | 0.730 | 0.730 | 0.730 | 0.731 |

1100 | 826.9 | 1520.3 | 0.734 | 0.735 | ||

1500 | 1226.9 | 2240.3 | 0.743 | 0.743 | ||

1900 | 1626.9 | 2960.3 | 0.742 | 0.742 |