Prandtl Number Calculator
Enter a fluid’s specific heat, dynamic viscosity, and thermal conductivity to calculate its Prandtl number.
What This Calculator Does
The Prandtl number is a dimensionless quantity that compares a fluid’s momentum diffusivity (how readily velocity differences spread) to its thermal diffusivity (how readily heat spreads). It’s used throughout heat transfer engineering to characterize convection behavior.
The Formula
The Prandtl number is Pr = (cp × μ) ÷ k, where cp is the fluid’s specific heat capacity at constant pressure, μ is its dynamic viscosity, and k is its thermal conductivity, all in consistent SI units.
- Pr < 1 (like liquid metals) means heat diffuses much faster than momentum.
- Pr ≈ 1 (like most gases) means heat and momentum diffuse at similar rates.
- Pr > 1 (like oils) means momentum diffuses much faster than heat, so the velocity boundary layer is thicker than the thermal boundary layer.
This is the standard heat-transfer definition of the Prandtl number, used for general engineering education and reference; fluid property values (cp, μ, k) should be taken at the relevant bulk or film temperature for accurate results.