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Reynolds number

The Reynolds number is a dimensionless number that tells you whether a flow is smooth and layered (laminar) or chaotic with eddies (turbulent). It expresses the ratio of inertial to viscous forces in the fluid, and determines which formula you use for the friction factor.

Re = \dfrac{\rho vD}{\mu}

Reynolds number in a pipe

Symbols

$\mu$	dynamic viscosity	Pa·s
$D$	pipe diameter	m
$Re$	Reynolds number

Example

Water ( $\rho = 1000$ kg/m³, $\mu = 10^{-3}$ Pa·s) flows at $v = 1.2$ m/s in a pipe with $D = 40$ mm. $Re = 1000\cdot 1.2\cdot 0.04/10^{-3} = 48.000$ .

Re

below about 2300 is laminar flow, above about 4000 is turbulent, with a transitional range in between.

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Part of Fluid Mechanics: Pipe flow and dimensionless numbers.