The Prandtl number decides whether heat or momentum spreads faster in a fluid. Liquid metals (Pr ≪ 1) conduct heat superbly; oils (Pr ≫ 1) carry momentum far more readily than heat. It is essential in convective heat-transfer correlations.
How to use the Prandtl Number Calculator
- Fluid
- Specific heat c_p
- Dynamic viscosity μ
- Thermal conductivity k
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose a fluid or enter custom properties.
Inputs explained
| Field | What to enter |
|---|---|
| Fluid | Choose one: Air (20 °C), Water (20 °C), Liquid sodium (400 °C), Methanol (20 °C) … |
| Specific heat c_p | Units: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C) |
| Dynamic viscosity μ | Units: Pa·s, mPa·s |
| Thermal conductivity k | Units: W/(m·K), BTU/(h·ft·°F) |
Example values
How the main result changes when Specific heat c_p changes and everything else stays at the example values above:
| Specific heat c_p (J/(kg·K)) | Prandtl number Pr |
|---|---|
| 502.5 | 0.7137 |
| 753.75 | 0.7137 |
| 1,005 | 0.7137 |
| 1,256.25 | 0.7137 |
| 1,507.5 | 0.7137 |
| 2,010 | 0.7137 |
Formula
Pr = c_p·μ / k = ν / α
Worked example
Inputs — Fluid: Air (20 °C).
Results — Prandtl number Pr = 0.71367.
Key terms
- Thermal diffusivity
- k/(ρc_p), how fast heat spreads.
Frequently asked questions
What is the Prandtl number of air?
About 0.71.
Why is Pr small for liquid metals?
They conduct heat extremely well.
How does Pr affect boundary layers?
High Pr gives a thermal boundary layer thinner than the velocity one.
Does Pr depend on temperature?
Yes, strongly for liquids such as oils.