# 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

## Formulas that use Reynolds Number

\(\large{ Re = \frac{ internal \; force }{ viscous \; force } }\) | |

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

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

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

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

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

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

### 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