# Prandtl Number

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

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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 (m^{2}/s)

α = thermal diffusivity (m^{2}/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^{o}F))

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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