Prandtl Number Calculator

Determine the Prandtl number of fluid using this Prandtl number calculator.

Prandtl number7.0073momentum diffuses faster than heat — water and most liquids

What it comparesmomentum diffusivity ÷ thermal diffusivitya dimensionless group is always a ratio of two competing effects, and the number tells you which is winning

FormulaPr = c_p µ ÷ k = ν ÷ α

Characteristic length used50 mmthe choice of length is a convention, so figures are only comparable when it matches

Flow speed2 m/s

Kinematic viscosity ν1.004e-6 m²/sµ ÷ ρ — 1.0038 centistokes

Note on this group A property of the fluid alone, not of the flow — which is unusual among these groups.

Reynolds number (Re)99,620.7585inertial forces ÷ viscous forces

Mach number (Ma)0.0014flow speed ÷ speed of sound

Froude number (Fr)2.8562inertia ÷ gravity

Knudsen number (Kn)1.36e-6molecular mean free path ÷ characteristic length

Weber number (We)2,742.3077inertia ÷ surface tension

Nusselt number (Nu)41.806convective heat transfer ÷ conductive heat transfer

Biot number (Bi)41.806surface convection ÷ internal conduction in the solid

Péclet number (Pe)698,072.3077advective transport ÷ diffusive transport

Check: Re × Pr698072equals the Péclet number exactly, by definition

The formula

each group is a ratio of two competing effects

Why physics is done in ratios

A dimensionless group compares two competing effects, and its value says which one is winning. That is far more useful than either quantity alone, because it means a model aircraft in a wind tunnel and a real one in flight behave the same way provided their groups match. This is dynamic similarity, and it is the entire basis of scale testing.

The thresholds are where the physics changes character. Reynolds 2300 in a pipe is where smooth flow gives way to turbulence. Mach 0.3 is where air stops behaving as incompressible. Froude 1 is where a free surface can support a hydraulic jump, exactly as Mach 1 is where a shock becomes possible. Knudsen 0.01 is where treating a gas as a continuous fluid stops being valid at all.

Two cautions. The characteristic length is a convention, not a measurement — pipe diameter, aerofoil chord, plate length — so two Reynolds numbers are only comparable when both used the same one. And Nusselt and Biot look identical as formulas; the difference is that Nusselt uses the fluid's conductivity and Biot the solid's, which makes them answer completely different questions.