Prandtl Number

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^oF)

k = thermal conductivity (W/m K, Btu/(h ft^2oF/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^oF

k = 0.06 (Btu/(h ft^2oF/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^oF / 0.06 (Btu/(h ft^2oF/ft)

= 302