Prandtl Number Calculator
Enter dynamic viscosity, specific heat and thermal conductivity to compute the Prandtl number Pr = μ·c_p/k.
Input Data
Results
At a glance:The Prandtl number Pr = μ·c_p/k = ν/α is a dimensionless group comparing momentum diffusivity ν = μ/ρ to thermal diffusivity α = k/(ρ·c_p). It indicates the relative thickness of the velocity and thermal boundary layers: Pr ≈ 1 (gases, e.g. air ~0.7) means they are similar; Pr ≫ 1 (oils, water ~7) means momentum diffuses much faster than heat (thick thermal boundary layer); Pr ≪ 1 (liquid metals) means heat diffuses faster. Pr appears in convection correlations (e.g. Nu = 0.023·Re^0.8·Pr^0.4) and boundary-layer theory. This tool computes Pr = μc_p/k from μ, c_p, k.
Formula
Pr = μ·c_p/k = ν/α
$$\mathrm{Pr} = \dfrac{\nu}{\alpha} = \dfrac{\mu\,c_p}{k}$$How to Use
- Enter dynamic viscosity μ, specific heat c_p and thermal conductivity k.
- The calculator returns Pr.
Case Studies
Air flow
μ = 1.8e-5, c_p = 1006, k = 0.026.
Pr = 1.8e-5×1006/0.026 ≈ 0.70.
Matches air; velocity & thermal BLs similar.
FAQ
What does Pr ≈ 1 mean?
Momentum and heat diffuse at similar rates, so velocity and thermal boundary layers have comparable thickness (typical of gases).
Why is water's Pr ~7 while air's is ~0.7?
Water has much higher density-specific heat product relative to its viscosity and conductivity, making thermal diffusion slower than momentum diffusion.
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References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.