# Prandtl Number

on . Posted in Dimensionless Numbers

Prandtl number, abbreviated as Pr, a dimensionless number, in fluid dynamics is used to calculate force by the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivities.  This number helps characterize the relative thickness of the velocity boundary layer to the thermal boundary layer.  Some common values of non-metallic thermal diffusivity values can be found here.

## Prandtl number formula

$$\large{ Pr = \frac{\nu}{\alpha} }$$
Symbol English Metric
$$\large{ Pr }$$ = Prandtl number $$\large{ dimensionless }$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity of the fluid $$\large{\frac{in^2}{sec}}$$ $$\large{\frac{mm^2}{s}}$$
$$\large{ \alpha }$$  (Greek symbol alpha) = thermal diffusivity of the fluid $$\large{\frac{in^2}{sec}}$$  $$\large{\frac{mm^2}{s}}$$

## Prandtl number formula

$$\large{ Pr = \frac{\mu\;Q}{k} }$$
Symbol English Metric
$$\large{ Pr }$$ = Prandtl number $$\large{ dimensionless }$$
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity of the fluid $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ Q }$$ = specific heat capacity of the fluid  $$\large{\frac{Btu}{lbm-F}}$$ $$\large{\frac{kJ}{kg-K}}$$
$$\large{ k }$$ = thermal conductivity of the fluid $$\large{ F }$$ $$\large{ K }$$