Turbulent Mixing in Pipe Flow

One way to mix two fluid streams is to have them flow together in a pipe, undergoing turbulent flow. 

A straight smooth pipe will produce turbulence (magnifying rather than damping out small disturbances) when the Reynolds number exceeds about 2100:

Re > 2100, where

Re = rho v D / µ

rho = gas density, 0.00121g/cm3 for air at 0C and 1 atm (STP)

v = mean velocity = volume flow rate / cross - section, cm/s

v = Q / (3.14/4) D² = pipe diameter, cm

µ = gas viscosity, 0.000181 poise for air at STP

A convenient way to re-write the equation for Re is

Re = rho ( 4 Q / 3.14 D²) D /  µ

Re = 4 rho Q / 3.14 D µ ,

which shows that for a given gas, Q / D determines Re.

For example, with Q = 2 L/min = 2000 cm3/60s = 33.3cm3/s and D = 0.1cm = 1mm, we have

Re = (4)(0.00121) (33.3) / (3.14)(0.1) (0.000181) Re = 2820, which is larger than 2100, so the flow is turbulent.

Mixing well requires a length greater than about ten diameters, L/D > 10.  

By:  Douglas W. Cooper, PhD