# Reynolds Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Reynolds number, abbreviated as Re, is a dimensionless number that measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces (the resistance to flow).

### Reynolds Number formula

$$\large{ Re = \frac{ \rho \; v \; l_c }{ \mu } }$$

$$\large{ Re = \frac{ v \; l_c }{ \nu } }$$

Where:

$$\large{ Re }$$ = Reynolds number

$$\large{ l_c }$$ = characteristic length or diameter of the fluid flow

$$\large{ \rho }$$  (Greek symbol rho) = fluid density

$$\large{ v }$$ = fluid velocity

$$\large{ \mu }$$  (Greek symbol mu)  = dynamic viscosity

$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity

Solve for:

$$\large{ l_c = \frac{ Re \; \mu }{\rho \; v } }$$

$$\large{ \rho = \frac{ Re \; \mu }{ l_c \; v } }$$

$$\large{ v = \frac{ Re \; \mu }{ \rho \; l_c } }$$

$$\large{ \mu = \frac{ \rho \; v \; l_c }{ Re } }$$