# Reynolds Number (Re)

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

**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.**

**Calculation (for circular pipes
only)**

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/m^{3})

μ=Dynamic viscosity (Pa.s)

## 2. Flow regimes ranges - laminar and turbulent

Re<2100 : laminar regime

2100<Re<4000 : intermediary regime

Re>4000 : turbulent regime

## 3. Reynolds number for stirred reactors

**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