Prandtl Number Calculator

Prandtl Number Calculator

Calculate the dimensionless Prandtl number (Pr) to characterize fluid flow and heat transfer.

Last updated: March 2026 | By ForgeCalc Engineering

Prandtl Number (Pr)
0.7114
Dimensionless

What is the Prandtl Number?

The Prandtl number (Pr) is a dimensionless number that represents the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It relates the thickness of the velocity boundary layer to the thermal boundary layer.

When Pr is small (e.g., in liquid metals), heat diffuses very quickly compared to momentum. When Pr is large (e.g., in heavy oils), momentum diffuses much faster than heat. For air at standard conditions, Pr is approximately 0.7.

The Formula

Prandtl Number Definition

Pr = (cₚ · μ) / k
  • cₚ = Specific heat capacity (J/kg·K)
  • μ = Dynamic viscosity (Pa·s)
  • k = Thermal conductivity (W/m·K)

Frequently Asked Questions

What is the Prandtl number for water?

At 20°C, the Prandtl number for water is approximately 7.0.

How does temperature affect Pr?

For most liquids, Pr decreases as temperature increases because viscosity drops significantly. For gases, Pr is relatively independent of temperature.

What does Pr = 1 mean?

If Pr = 1, the momentum and thermal boundary layers have the same thickness, and heat and momentum diffuse at the same rate.

Is Pr used in turbulent flow?

Yes, Pr is a key parameter in heat transfer correlations for both laminar and turbulent flows (e.g., the Dittus-Boelter equation).

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