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 (m2/s)
α = thermal diffusivity (m2/s)
The Prandtl number can alternatively be expressed as
Pr = μ cp / k (2)
where
μ = absolute or dynamic viscosity (kg/m s, lbm/(ft h))
cp = specific heat (J/kg K, Btu/(lbm oF))
k = thermal conductivity (W/m K, Btu/(h ft2 oF/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)
cp = 0.50 Btu/(lbm oF)
k = 0.06 (Btu/(h ft2 oF/ft)
Dynamic viscosity can be converted from cP to lbm/(ft h) as
μ = 15 (cP) (2.4191 (lbm/(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/(lbm oF) / 0.06 (Btu/(h ft2 oF/ft)
= 302
