Prandtl Number Calculator: Pr from Viscosity, Heat Capacity and Conductivity

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Resistance of the fluid to shear flow. Water at 20 °C is about 0.001 Pa·s; engine oil about 0.8 Pa·s.
Pa·s
Energy needed to raise 1 kg of the fluid by 1 kelvin at constant pressure. Water is about 4182 J/(kg·K).
J/(kg·K)
How readily the fluid conducts heat. Water is about 0.598 W/(m·K); air about 0.026 W/(m·K).
W/(m·K)
Choose which quantity to solve for. Enter the other three values, including a known Pr for reverse solves.
Enter the known Prandtl number when solving for viscosity, heat capacity or conductivity. Ignored when solving for Pr directly.
Prandtl Number (Pr)Low-Pr liquid
7.0073

Ratio of momentum diffusivity to thermal diffusivity

Heat transfer regimeLow-Pr liquid (water range) - moderate thermal resistance
7.0073
Liquid metal<0.05Gas0.05-1Low-Pr liquid1-10Moderate liquid10-100High-Pr oil100+

Pr = 7.0073: low-Pr liquid - momentum diffusion moderately dominates.

  • Water at 20 °C has Pr approximately 6.9, typical of low-to-moderate Prandtl number liquids.
  • The thermal boundary layer is thinner than the velocity boundary layer.
  • Standard Nusselt correlations (Dittus-Boelter, Gnielinski) work well in this range for turbulent pipe flow.

Next stepUse the Gnielinski correlation (Nu = (f/8)(Re - 1000)Pr / [1 + 12.7(f/8)^0.5(Pr^(2/3) - 1)]) for turbulent pipe flow.

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