Calculate the Prandtl number from fluid properties. Compare thermal and momentum diffusivities, boundary layer ratios, and regime classification for heat transfer analysis.
The Prandtl number (Pr = ν/α = µCp/k) is a dimensionless number that compares momentum diffusivity (kinematic viscosity ν) to thermal diffusivity (α). It tells you the relative thickness of the velocity and thermal boundary layers and determines which Nusselt number correlation to use.
For gases (Pr ≈ 0.7), heat and momentum diffuse at similar rates and boundary layers have similar thickness. For water (Pr ≈ 7), momentum diffuses faster — the velocity boundary layer is thicker. For oils (Pr > 100-1000), the thermal boundary layer is much thinner than the velocity boundary layer.
This calculator computes Pr from viscosity, specific heat, and thermal conductivity. It also calculates the thermal diffusivity, kinematic viscosity, and boundary layer thickness ratio (δ_v/δ_T ≈ Pr^(1/3)). Preset buttons load properties for water, air, engine oil, mercury, and ethylene glycol.
A reference table lists Prandtl numbers for seven common fluids from liquid metals (Pr ≈ 0.01) to glycerin (Pr ≈ 12,500), spanning five orders of magnitude.
The Prandtl number is the first thing you need to know when selecting a Nusselt correlation for heat transfer analysis. This calculator provides it instantly from fluid properties.
The boundary layer regime classification and visual scale help build intuition for how different fluids behave in convective heat transfer. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain.
Pr = µCp/k = ν/α. Thermal diffusivity: α = k/(ρCp). Kinematic viscosity: ν = µ/ρ. BL ratio: δ_v/δ_T ≈ Pr^(1/3).
Result: Pr = 7.01, α = 1.43×10⁻⁷ m²/s, ν = 1.00×10⁻⁶ m²/s
Pr = 0.001002 × 4182 / 0.598 = 7.01. Water at 20°C: momentum diffuses ~7× faster than heat. BL ratio = 7.01^(1/3) = 1.91.
Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.
Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes
Use concise notes to keep each section focused on outcomes. ## Practical Notes
Check assumptions and units before interpreting the number. ## Practical Notes
Capture practical pitfalls by scenario before sharing the result. ## Practical Notes
Use one example per section to avoid misapplying the same formula. ## Practical Notes
Document rounding and precision choices before you finalize outputs. ## Practical Notes
Flag unusual inputs, especially values outside expected ranges. ## Practical Notes
Apply this as a quality checkpoint for repeatable calculations.
Pr appears in all forced-convection Nusselt number correlations. It determines the relative effectiveness of convective heat transfer. Nu ∝ Pr^n where n is typically 1/3 to 0.4.
When Pr = 1, velocity and thermal boundary layers have equal thickness. Heat and momentum diffuse at the same rate. This is nearly true for gases (air: Pr = 0.71).
Liquid metals have high thermal conductivity (due to free electrons) and low viscosity, giving α >> ν. The thermal boundary layer extends far beyond the velocity boundary layer.
Water Pr drops dramatically with temperature: Pr ≈ 13 at 0°C, 7 at 20°C, 3 at 60°C, 1.75 at 100°C. This is mostly because viscosity decreases while k increases.
Air has Pr ≈ 0.71 at room temperature and this barely changes with temperature (0.70-0.72 from 0 to 400°C). This is because µ, Cp, and k all change similarly with temperature for gases.
The Schmidt number (Sc = ν/D) is the mass transfer analog of Pr. Their ratio is the Lewis number: Le = Sc/Pr = α/D. When Le = 1, heat and mass transfer are analogous.