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Prandtl Number

A dimensionless number approximating the ratio of momentum diffusivity to thermal diffusivity.

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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 c p / k                                    (2)

where

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

c p = specific heat (J/kg K, Btu/(lb m o F))

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

c p = 0.50 Btu/(lb m o F)

k = 0.06 (Btu/(h ft2 o F/ft)

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

μ = 15 (cP) ( 2.4191 (lb m /(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/(lb m o F) / 0.06 (Btu/(h ft2 o F/ft)

= 302

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Related Topics

  • Fluid Mechanics

    The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

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