Reynolds Number
Reynolds number, abbreviated as Re, is a dimensionless number that 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
Tags: Equations for Flow Equations for Viscosity Equations for Orifice and Nozzle