 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/m3)
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