Reynolds Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

reynolds number 1Reynolds 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 \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\)

 

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Tags: Equations for Flow Equations for Viscosity Equations for Orifice and Nozzle