# Reynolds Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers Reynolds number, abbreviated as Re, a dimensionless number, measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces (the resistance to flow).

## Reynolds Number Range

Laminar flow = up to Re = 2300

Transition flow = 2300 < Re < 4000

Turbulent flow = Re > 4000

## Reynolds Number formulas

 $$\large{ Re = \frac{ internal \; force }{ viscous \; force } }$$ $$\large{ Re = \frac{ \rho \; v \; l_c }{ \mu } }$$ $$\large{ Re = \frac{ v \; l_c }{ \nu } }$$ $$\large{ Re = \frac{ U \; l_c }{ \mu } }$$ $$\large{ Re = \frac{ \bar {v} \; d \; \rho}{ \mu } }$$ $$\large{ Re = \frac{ \bar {v} \; d }{ \nu } }$$ $$\large{ Re = \frac{ 4 \; Q }{ \pi \; d \; \bar {v} } }$$

### Where:

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

$$\large{ \bar {v} }$$ = average velocity

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

$$\large{ U }$$ = characteristic velocity

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

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

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

$$\large{ \pi }$$ = Pi

$$\large{ d }$$ = pipe inside diameter

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

$$\large{ Q }$$ = volumetric flow rate