How to Use Prandtl Number Calculator
The Prandtl Number Calculator determines the dimensionless ratio that governs the relative thickness of velocity and thermal boundary layers, accepting either transport-property-form (ν, α) or fluid-property-form (μ, Cp, k) inputs.
- Select input mode — choose “Kinematic (ν, α)” if you have tabulated diffusivity values, or “Property (μ, Cp, k)” if you are working directly with fluid property data sheets.
- Enter kinematic viscosity ν (mode 1) or dynamic viscosity μ (mode 2) — ν = μ/ρ; SI units are m²/s and Pa·s respectively.
- Enter thermal diffusivity α (mode 1) or thermal conductivity k and specific heat Cp (mode 2).
- Read Pr and its physical interpretation — the result panel classifies the fluid as a liquid metal (Pr ≪ 1), gas (Pr ≈ 1) or viscous liquid (Pr ≫ 1).
- Use Pr in heat-transfer correlations — Nusselt number correlations such as Dittus–Boelter (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴) require Pr as a key input alongside Re.
Formula & Theory — Prandtl Number Calculator
The Prandtl Number Calculator computes Pr from two equivalent formulations:
Pr = ν / α (kinematic form)
Pr = μ · Cp / k (property form)
α = k / (ρ · Cp) (thermal diffusivity definition)
δ_t / δ_v ≈ Pr^(-1/3) (boundary-layer thickness ratio)| Symbol | Meaning | SI Unit |
|---|---|---|
| Pr | Prandtl number (dimensionless) | — |
| ν | Kinematic viscosity | m²/s |
| α | Thermal diffusivity | m²/s |
| μ | Dynamic viscosity | Pa·s |
| Cp | Isobaric specific heat capacity | J/(kg·K) |
| k | Thermal conductivity | W/(m·K) |
Reference values: liquid mercury Pr ≈ 0.025 (very thin thermal boundary layer); air ≈ 0.71; water 20 °C ≈ 6.9; engine oil 20 °C ≈ 6400 (very thick thermal BL relative to velocity BL). Prandtl number of ideal gases is nearly independent of pressure and changes only slowly with temperature.
Use Cases for Prandtl Number Calculator
- Forced convection design — use Pr in Dittus–Boelter, Gnielinski or Colburn correlations to predict tube-side or flat-plate heat-transfer coefficients in heat exchangers.
- Heat-exchanger fluid selection — compare Pr of candidate working fluids (water, glycol, mineral oil, liquid metals) to select fluids that maximise heat-transfer performance.
- CFD turbulence modelling — the turbulent Prandtl number Pr_t ≈ 0.85–0.9 governs the eddy thermal diffusivity term in RANS-based energy transport equations.
- Natural convection analysis — combine Pr with the Grashof number to form the Rayleigh number Ra = Gr·Pr, used in free-convection Nusselt correlations for vertical plates and cylinders.
- Liquid-metal cooling systems — nuclear reactor and high-power electronics cooling with liquid sodium or lithium–lead (Pr ≈ 0.003–0.03) requires special low-Pr Nu correlations (e.g. Lubarsky–Kaufman).
- Educational dimensional analysis — illustrate how Pr bridges momentum and energy transport and how it controls the dominant resistance (thermal or hydrodynamic) in boundary layers.