# Dean Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Dean number, abbreviated as De, a dimensionless number, used in momentum transfer for the flow in curved pipes and channels.  The equation and calculation is shown below.

## Dean Number formula

 $$\large{ De = \sqrt { \frac {d}{2 \; r} } \; \frac {\rho \; v \; d}{ \mu } = \sqrt { \frac { d } { 2 \; r } } \; Re }$$

### Where:

 Units English Metric $$\large{ De }$$ = Dean number $$\large{dimensionless}$$ $$\large{ \rho }$$  (Greek symbol rho) = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ d }$$ = diameter $$\large{in}$$ $$\large{mm}$$ $$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$ $$\large{ r }$$ = radius of curviture of the path of channel $$\large{in}$$ $$\large{mm}$$ $$\large{ Re }$$ = Reynolds number $$\large{dimensionless}$$ $$\large{ v }$$ = axial velocity scale $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$