 # Reynolds Number (Re)

## Definition, calculation and reference values of the Reynolds Number

Follow us on Twitter 1. Reynolds number definition and calculation formula
2. Flow regimes - laminar and turbulent
3. Reynolds number for stirred reactors

## 1. Reynolds number definition and calculation formula

### What is the Reynolds number ?

The Reynolds number compares the inertial forces to the viscous forces that apply to a fluid. It is a dimensionless number used to determine if a fluid flow will be turbulent or laminar.
A low Reynolds number means that the viscosity dominates and the flow will be laminar. At high Reynolds number, the inertial forces dominate leading to a turbulent flow.

### How to calculate the Reynolds number ?

Calculation (for circular pipes only) : Re = D.u.ρ/μ Re=Reynolds number for circular pipe (adimensional)
D=diameter of pipe (m)
<u>=mean velocity (straight section) (m/s)
ρ=Volumic mass of the liquid (kg/m3)
μ=Dynamic viscosity (Pa.s)

## 2. Flow regimes ranges - laminar and turbulent

### What is the Reynolds number in laminar flow or turbulent flow ?

Re<2100 : laminar regime
2100<Re<4000 : intermediary regime
Re>4000 : turbulent regime

## 3. Reynolds number for stirred reactors

The concept of Reynolds number can be applied in many areas of fluid dynamics, with some slight adaptation of the formula. The formula below is for example giving the Reynolds number for stirred reactor Re<10 : laminar regime
10<Re<10000 : intermediary regime
Re>10000 : turbulent regime

D=diameter of agitator (m)
N=agitator speed (rps)

Source

Mecanique et Rheologie des fluides en genie chimique, Noel Midoux, Lavoisier Tec et Doc, page 139, page 246