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 (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, lb_{m}/(ft h))
c_{p} = specific heat (J/kg K, Btu/(lb_{m} ^{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
 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 ft^{2} ^{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 ft^{2} ^{o}F/ft)
= 302
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