# 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

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

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

$$\large{ Re = \frac{ U \; l_c }{ \mu } }$$

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

$$\large{ Re = \frac{ \bar {v} \; d }{ \nu } }$$

$$\large{ Re = \frac{ 4 \; Q }{ \pi \; d \; \bar {v} } }$$

Symbol English Metric
$$\large{ Re }$$ = Reynolds number $$\large{ dimensionless }$$
$$\large{ \bar {v} }$$ = average velocity $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$
$$\large{ l_c }$$ = characteristic length or diameter of fluid flow  $$\large{ in }$$ $$\large{ mm }$$
$$\large{ U }$$ = characteristic velocity $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$
$$\large{ \rho }$$  (Greek symbol rho) = density of fluid $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{kg}{m^3} }$$
$$\large{ \mu }$$  (Greek symbol mu)  = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity $$\large{ \frac{in^2}{sec} }$$ $$\large{ \frac{mm^2}{s} }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ d }$$ = pipe inside diameter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ v }$$ = velocity of fluid $$\large{ \frac{ft}{sec} }$$ $$\large{ \frac{m}{s} }$$
$$\large{ Q }$$ = volumetric flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$ 