Prandtl Number Calculator
Calculate Prandtl number for air, water or any fluid from viscosity, specific heat, and thermal conductivity. Free fluid dynamics heat transfer calculator.
About This Calculator
The Prandtl number calculator computes the dimensionless Prandtl number (Pr) for any fluid using its dynamic viscosity (μ), specific heat capacity (Cp), and thermal conductivity (k). The Prandtl number is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity, expressed as Pr = μ × Cp / k. This dimensionless quantity is fundamental in fluid mechanics and heat transfer analysis, helping engineers and scientists determine whether heat diffusion occurs primarily through conduction or convection.
The calculator offers preset values for air (Pr ≈ 0.715 at 20°C) and water (Pr ≈ 6.9 at 20°C), or you can enter custom values for any fluid. When you provide the fluid density, the calculator also computes the kinematic viscosity (ν = μ / ρ) and thermal diffusivity (α = k / (ρ × Cp)), giving you a complete picture of the fluid's transport properties. The Prandtl number result comes with an interpretation of whether conduction or convection dominates heat transfer in that fluid.
Regional notes: The Prandtl number is a fluid property independent of geographic region. The values for common fluids (air, water) are standard measurements accepted worldwide and do not vary by country. For localized engineering applications, users should enter fluid properties at their specific temperature and pressure conditions, as fluid properties vary with temperature. This calculator is used globally in mechanical engineering, aerospace engineering, chemical engineering, and HVAC design.
Frequently Asked Questions
What is the Prandtl number?
The Prandtl number (Pr) is a dimensionless number that approximates the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is calculated as Pr = μ × Cp / k, where μ is dynamic viscosity, Cp is specific heat capacity, and k is thermal conductivity. It helps determine whether heat transfer via conduction or convection is more dominant in a fluid.
How do you calculate the Prandtl number?
The Prandtl number is calculated using the formula Pr = μ × Cp / k, where μ is the dynamic viscosity in Pa·s, Cp is the specific heat capacity in J/(kg·K), and k is the thermal conductivity in W/(m·K). Alternatively, Pr = ν / α, where ν is kinematic viscosity and α is thermal diffusivity.
What is the Prandtl number of water?
The Prandtl number of water at 20°C is approximately 6.9. For dynamic viscosity of 1.002 mPa·s, thermal conductivity of 0.607 W/(m·K), and specific heat of 4184 J/(kg·K), the Prandtl number is Pr = 0.001002 × 4184 / 0.607 = 6.90. This means convection dominates over conduction in water.
What is the Prandtl number of air?
The Prandtl number of air at room temperature is approximately 0.715. For dynamic viscosity of 0.0182 mPa·s, thermal conductivity of 0.0256 W/(m·K), and specific heat of 1006 J/(kg·K), the Prandtl number is Pr = 0.0000182 × 1006 / 0.0256 = 0.715. This means conduction and convection contribute similarly in air.
What does a Prandtl number less than 1 mean?
A Prandtl number less than 1 (Pr < 1) means thermal diffusivity exceeds momentum diffusivity, indicating that heat conduction is faster than momentum transfer. Fluids like air (Pr ≈ 0.7) and liquid metals (Pr ≈ 0.01–0.1) fall in this category, where conductive heat transfer is more significant than convective.
What is the physical significance of the Prandtl number?
The Prandtl number relates the thickness of momentum boundary layer to thermal boundary layer in fluid flow. When Pr > 1, the momentum boundary layer is thicker than the thermal boundary layer, meaning convective heat transfer dominates. When Pr < 1, the thermal boundary layer is thicker, meaning conductive heat transfer dominates. For Pr ≈ 1, both boundary layers have similar thickness.
How do I use the Prandtl number calculator for custom fluids?
Select the Custom option from the Fluid dropdown and enter the dynamic viscosity in mPa·s, specific heat capacity in J/(kg·K), and thermal conductivity in W/(m·K). Optionally enter the fluid density to also calculate kinematic viscosity and thermal diffusivity. The calculator will compute the Prandtl number and classify the dominant heat transfer mode.
What are typical Prandtl numbers for common fluids?
Typical Prandtl number ranges: Air 0.7–0.73, Water 6.9, Seawater 7.2–13.4, Engine oil 100–40,000, Glycerin 12,500, Mercury 0.015, Sodium 0.004, Helium 0.66, Oxygen 0.63, Argon 22.7. Liquids generally have higher Pr values than gases due to higher viscosity relative to thermal conductivity.