Prandtl Number

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The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) and 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 c_p / k         (2)

where

μ = absolute or dynamic viscosity (kg/m s, cP)

c_p = specific heat capacity (J/kg K, Btu/(lb ^oF))

k = thermal conductivity (W/m K, Btu/(h ft^{2 o}F/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
• water - Pr ranges 1 - 10
• liquid metals - Pr ranges 0.001 - 0.03
• oils - Pr ranges 50 - 2000

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Related Topics

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

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