# Reynolds Number

Written by Jerry Ratzlaff. Posted in Dimensionless Numbers

Reynolds number is a dimensionless ratio used extensively in flow correlations and "loss" computations.  Reynolds number is very important and probably most frequently used non-dimension number in fluid dynamics. To find out if the flow of gas, air, water or any other fluid is laminar or turbulent calculation of Reynolds number is necessary.

Reynolds number is one of the most frequently used dimensionless number to find the fluid's flow regime.  The Reynolds number is often regarded as the ratio of inertial forces to viscous forces - the tendency to keep moving versus the tendency to slow down.

Fluid flow can be laminar flow or turbulent flow.

Laminar flow: Re < 2000

Transitional flow: 2000 < Re < 4000

Turbulent flow: Re > 4000

## formula

$$Re = \frac{ v d} {\nu} = \frac{\rho v d} {\mu}$$

Where:

$$Re$$ = Reynolds number

$$v$$ = velocity

$$d$$ = inside pipe diameter

$$\nu$$ (Greek symbol nu) = kinematic viscosity

$$\rho$$ (Greek symbol rho) = density

$$\mu$$ (Greek symbol mu) = dynamic viscosity