# Reynolds number (for a flow in a tube)

## Description

In fluid mechanics, the Reynolds number is used to help predict if flow will be laminar or turbulent. We know that flow in a very smooth tube, streamlined object will be laminar at low velocity. We also know that at high velocity, even flow in a smooth tube will experience turbulence. At intermediate velocities, flow may oscillate back and forth indefinitely between laminar and turbulent. Reynolds number is an indicator which can reveal whether flow is laminar or turbulent.

Experiments have revealed that Reynolds number is related to the onset of turbulence. For Reynolds number below about **2000**, flow is laminar; above about **3000**, flow is turbulent. For values of Reynolds number between about **2000 and 3000**, flow is unstable. It can be laminar, but small obstructions and surface roughness can make it turbulent, and it may oscillate randomly between being laminar and turbulent. The blood flow through most of the body is a quiet, laminar flow.

## Variables

R_{e} | Reynolds number (dimensionless) |

ρ | Density of the fluid (kg/m^{3}) |

v | Mean velocity of the fluid (m/s) |

D_{H} | Hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m) |

μ | Dynamic viscosity of the fluid (Pa*s) |