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# Prandtl Number

## 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. Involving 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 pressure - SI units.
• ### Ammonia - Prandtl Number vs. Temperature and Pressure

Figures and table with changes in Prandtl number for ammonia with changes in temperature and pressure.
• ### Carbon Dioxide - Liquid Properties

Properties of saturated liquid Carbon Dioxide - CO2 - density, specific heat, kinematic viscosity, thermal conductivity and Prandtl number.
• ### Dimensionless Numbers

Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more.
• ### Dry Air - Thermodynamic and Physical Properties

Thermodynamic properties of dry air - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity at temperatures ranging 175 - 1900 K.
• ### Methane - Prandtl number vs. Temperature

Figures and table showing changes in Prandtl number for methane with changes in temperature and pressure.
• ### Nitrogen - Prandtl number vs. Temperature and Pressure

Figures and tables showing Prandtl number of nitrogen at varying temperarure and pressure, SI and Imperial units.
• ### Propane - Prandtl Number vs. Temperature and Pressure

Figures and tables with 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 at different temperatures like density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more.

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## Citation

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

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9.19.12