where ¯u is the mean flow velocity and d the pipe diameter
(characteristic length) and ν the kinematic viscosity.
For general engineering purposes, the following values are
appropriate: pipe flow is laminar if the Reynolds number
is approximately 2000. The flow in a pipe is turbulent if
the Reynolds number is greater than approximately 4000.
For Reynolds numbers between these two limits, the flow
switches rapidly between laminar and turbulent conditions,
this is known as the transition regime. The Schmidt number
is governed by the ratio of momentum transfer to mass
transfer by molecular diffusion,