Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

# Prandtl Number

## The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity to thermal diffusivity

The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity - and can be expressed as

Pr = v / α                                     (1)

where

Pr = Prandtl's number

v = momentum diffusivity (m2/s)

α = thermal diffusivity (m2/s)

The Prandtl number can alternatively be expressed as

Pr = μ cp / k                                    (2)

where

μ = absolute or dynamic viscosity (kg/m s, lbm/(ft h))

cp = specific heat (J/kg K, Btu/(lbm oF))

k = thermal conductivity (W/m K, Btu/(h ft2 oF/ft))

The Prandtl Number is often used in heat transfer and free and forced convection calculations. It depends on the fluid properties.

• gases - Pr ranges 0.7 - 1.0
• dry air
• water - Pr ranges 1 - 10
• liquid metals - Pr ranges 0.001 - 0.03
• oils - Pr ranges 50 - 2000

### Example - Calculation of a Prandtl Number

μ = 15 (cP)

cp = 0.50 Btu/(lbm oF)

k = 0.06 (Btu/(h ft2 oF/ft)

Dynamic viscosity can be converted from cP to lbm/(ft h) as

μ = 15 (cP) (2.4191 (lbm/(ft hr)) / (1 cP))

= 36.3 lb/(ft hr)

The Prandtl Number can be calculated as

Pr = 36.3 (lb/(ft hr)) 0.50 Btu/(lbm oF)0.06 (Btu/(h ft2 oF/ft)

= 302

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

## Related Documents

• Air Properties - Imperial Units - Thermodynamic properties of air at low pressures - imperial units
• Air Properties - SI Units - Ideal gas properties of air at low pressures - in SI units
• Ammonia - Prandtl Number - Figures and table showing changes in Prandtl number for ammonia with changes in temperature and pressure
• Carbon Dioxide Properties - Properties of saturated liquid Carbon Dioxide - CO2 - density, specific heat, kinematic viscosity, thermal conductivity and Prandtl number
• Dimensionless numbers - Definitions and symbols for physical and chemical dimensionless quantities, with areas of application of the different numbers. Reynolds, Euler, Nusselt, Prandtl..... and many more
• Dry Air Properties - Dry air properties at temperatures ranging 175 - 1900 K - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity
• Methane - Prandtl number - Figures and table showing changes in Prandtl number for methane with changes in temperature and pressure
• Nitrogen - Prandtl number - Figures and tables showing Prandtl number of nitrogen at varying temperarure and pressure, SI and Imperial units
• Propane - Prandtl Number - Figures and tables showing Prandtl Number of liquid and gaseous propane at varying temperarure and pressure, SI and Imperial units
• Reynolds Number - Introduction and definition of the dimensionless Reynolds Number - online calculators
• Water - Thermophysical Properties - Thermal properties of water - density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more

## Tag Search

• en: prandtl number convection heat transfer
• es: número de Prandtl transferencia de calor por convección
• de: Prandtl-Zahl Konvektionswärmeübertragung

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

## Citation

• Engineering ToolBox, (2009). Prandtl Number. [online] Available at: https://www.engineeringtoolbox.com/prandtl-number-d_1068.html [Accessed Day Mo. Year].

Modify access date.

. .

#### Scientific Online Calculator 10 23