Reynolds Number

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

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

\(\large{ Re = \frac{ v \; l_c }{ \nu }  }\)

\(\large{ Re = \frac{ U \; l_c }{ \mu }  }\)

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

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

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

Where:

Units	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	\(\large{\frac{ft^3}{sec}}\)	\(\large{\frac{m^3}{s}}\)