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 in the fluid flow (the resistance to flow). 

The Reynolds number is commonly used in fluid dynamics to predict the onset of turbulence in a fluid flow.  At low Reynolds numbers (less than about 2300 for a pipe flow), the flow is laminar and exhibits smooth, ordered flow.  At high Reynolds numbers (greater than about 4000 for a pipe flow), the flow becomes turbulent and exhibits chaotic, irregular flow patterns.  The transition between laminar and turbulent flow depends on the specific system and the properties of the fluid.

 

Reynolds Number Range

• Laminar flow = up to Re = 2300
• Transition flow = 2300 < Re < 4000
• Turbulent flow = Re > 4000

 

Reynolds number formula
\(\large{ Re = \frac{ \rho \; v \; l_c }{ \mu }  }\)
Symbol	English	Metric
\(\large{ Re }\) = Reynolds number	\(\large{ dimensionless }\)
\(\large{ \rho }\)  (Greek symbol rho) = density of the fluid	\(\large{ \frac{lbm}{ft^3} }\)	\(\large{ \frac{kg}{m^3} }\)
\(\large{ v }\) = velocity of the fluid	\(\large{ \frac{ft}{sec} }\)	\(\large{ \frac{m}{s} }\)
\(\large{ l_c }\) = characteristic length or diameter of fluid flow	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ \mu }\)  (Greek symbol mu)  = dynamic viscosity of the fluid	\(\large{\frac{lbf-sec}{ft^2}}\)	\(\large{ Pa-s }\)

 

Reynolds number formula
\(\large{ Re = \frac{ v \; l_c }{ \nu }  }\)
Symbol	English	Metric
\(\large{ Re }\) = Reynolds number	\(\large{ dimensionless }\)
\(\large{ v }\) = velocity of the fluid	\(\large{ \frac{ft}{sec} }\)	\(\large{ \frac{m}{s} }\)
\(\large{ l_c }\) = characteristic length or diameter of the fluid flow	\(\large{ in }\)	\(\large{ mm }\)
\(\large{ \nu }\)  (Greek symbol nu) = kinematic viscosity	\(\large{ \frac{in^2}{sec} }\)	\(\large{ \frac{mm^2}{s} }\)