## Prandtl Number Calculator

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## Prandtl Number Equation

The Prandtl Number (Pr) called also Prandtl group is a dimensionless number, introduced by the physicist Ludwig Prandtl.

The Prandtl Number equation/formula is the ratio of two transport properties, the kinematic viscosity and the thermal diffusivity. The first propritie affect the the velocity distribution and the second property affect the velocity distribution.

In other words it evaluate the relation between the two main properties the momentum transport and thermal transport capacity of a fluid.

Pr =

v/ α (1)Where :

v : momentum diffusivity, (kinematic viscosity).α

: thermal diffusivity.Can also expressed :

Pr

= μ cp / k(2)Where :

c: specific heat, (SI units: J/kg·K)._{p}μ : dynamic viscosity, (SI units: Pa s = N s/m2)

Prandtl Number equation

k: thermal conductivity, (SI units: W/m·K)

Prandtl Number ranging :

- Liquid Metals from 0.005 to 0.01.
- Gases from 0.6 to 1.
- oils some up to 5000 and more.

## Prandtl Number Significance

Prandtl number signafice two things:

- The relative thickness of the velocity and thermal boundary layer.
- How fast the thermal diffusion takes place in comparison to momentum diffusion.

**Pr < 1** , when the Pr is small (Pr<1), the temperature gradient near a surface is less steep than the velocity gradient which mean that **momentum diffusion < thermal diffusion**. The thermal diffusion is dominant in comparison with momentum diffusion as per the above image.

Pr > 1, when the Pr is large (Pr>1), the temperature gradient near the surface is is steeper than the velocity gradient which mean **momentum diffusion > thermal diffusion**. The momentum diffusion is dominant in comparison with the thermal diffusion as shown in the above image.

## Prandtl Number Table

### Prandtl Number of Water

Prandtl Number of Water at atmospheric pressure

T( C) | μ (Pa s) | Cp(J/kg K) | k(W/m K) | Pr |

10 | 0.001307 | 4188 | 0.5674 | 9.642 |

15 | 0.001138 | 4184 | 0.5769 | 8.253 |

20 | 0.001002 | 4183 | 0.5861 | 7.152 |

25 | 0.0008905 | 4183 | 0.5948 | 6.263 |

30 | 0.0007977 | 4183 | 0.603 | 5.534 |

35 | 0.0007196 | 4183 | 0.6107 | 4.929 |

40 | 0.0006533 | 4182 | 0.6178 | 4.422 |

45 | 0.0005963 | 4182 | 0.6244 | 3.994 |

50 | 0.0005471 | 4181 | 0.6305 | 3.628 |

55 | 0.0005042 | 4182 | 0.636 | 3.315 |

60 | 0.0004666 | 4183 | 0.641 | 3.045 |

65 | 0.0004334 | 4184 | 0.6455 | 2.81 |

70 | 0.000404 | 4187 | 0.6495 | 2.605 |

75 | 0.0003779 | 4190 | 0.653 | 2.425 |

80 | 0.0003545 | 4194 | 0.6562 | 2.266 |

85 | 0.0003335 | 4199 | 0.6589 | 2.125 |

90 | 0.0003145 | 4204 | 0.6613 | 2 |

95 | 0.0002974 | 4210 | 0.6634 | 1.888 |

100 | 0.00001227 | 2042 | 0.02506 | 0.9996 |

For a different pressure you can always use our online Prandtl Number calculator on the top.

### Prandtl Number of Air

Prandtl Number of Air dry at atmospheric pressure.

T ( C) | T (F) | Prandtl Number, Pr |

0 | 32 | 0.71 |

20 | 68 | 0.71 |

40 | 104 | 0.71 |

60 | 140 | 0.71 |

80 | 176 | 0.71 |

100 | 212 | 0.71 |

200 | 392 | 0.71 |

300 | 572 | 0.71 |

400 | 752 | 0.72 |

500 | 932 | 0.72 |

1000 | 1832 | 0.74 |

### Prandtl Number of Carbon Dioxide

Prandtl Number of Carbon Dioxide at atmospheric pressure.

T ( C) | T (F) | Prandtl Number, Pr |

-53 | -63 | 0.818 |

-23 | -9 | 0.793 |

27 | 81 | 0.770 |

77 | 171 | 0.755 |

127 | 261 | 0.738 |

177 | 351 | 0.721 |

227 | 441 | 0.702 |

277 | 531 | 0.685 |

327 | 621 | 0.668 |

## Prandtl Number of Liquid Organic Compounds

Organic compounds at 20 °C, 68 °F

Liquid | Prandtl Number, Pr |

Acetic acid | – |

Acetone | 3.97 |

Chloroform | 4.35 |

Ethyl Acetate | 6.59 |

Ethyl Alcohol | 16.29 |

Ethylene Glycol | 183.7 |

Glycerol | – |

n-Heptane | 6.48 |

n-Hexane | 4.4 |

For a different pressure and temperature you can always use our online Prandtl Number calculator on the top.

Reference: