Prandtl Number Calculator

What is Prandtl Number?

The Prandtl number (Pr) is a dimensionless quantity that relates the rate of momentum diffusion to the rate of thermal diffusion in a fluid. It is defined as the ratio of kinematic viscosity (ν) to thermal diffusivity (α). This number is fundamental in heat transfer analysis as it determines the relative thickness of the velocity and thermal boundary layers.

Prandtl Number Formula

The Prandtl number is calculated using the formula:

Pr = ν / α

Where:

• Pr = Prandtl number (dimensionless)
• ν = Kinematic viscosity (m²/s)
• α = Thermal diffusivity (m²/s)

How to Use the Calculator

Select the variable you want to solve for from the dropdown menu:

• Solve for Prandtl Number (Pr): Enter kinematic viscosity and thermal diffusivity to calculate Pr.
• Solve for Kinematic Viscosity (ν): Enter Prandtl number and thermal diffusivity to find kinematic viscosity.
• Solve for Thermal Diffusivity (α): Enter kinematic viscosity and Prandtl number to find thermal diffusivity.

Typical Prandtl Number Values

Different fluids have characteristic Prandtl number ranges:

• Air (20°C): Pr ≈ 0.71 — heat diffuses faster than momentum
• Water (20°C): Pr ≈ 7.0 — momentum diffuses faster than heat
• Engine oil (60°C): Pr ≈ 1000 — very high, velocity boundary layer dominates
• Liquid mercury: Pr ≈ 0.025 — very low, thermal diffusion dominates
• Helium: Pr ≈ 0.66 — similar to air

Applications of Prandtl Number

Engineers use the Prandtl number in various applications:

• Heat exchanger design using Nusselt number correlations (Dittus-Boelter, Sieder-Tate)
• HVAC system analysis for cooling coils and duct heaters
• Nuclear reactor cooling with liquid metal coolants
• Computational fluid dynamics (CFD) simulations
• Food processing heat penetration analysis

Also check: Reynolds Number Calculator, Nusselt Number Calculator, Peclet Number Calculator, Schmidt Number Calculator, Thermal Conductivity Calculator, Specific Heat Calculator.