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Reynolds number

The Reynolds number is given by:

\[{\mathop{\rm Re}\nolimits} = \frac{{\rho uL}}{\eta } = \frac{{uL}}{\nu }\]

where u is the velocity, L is a characteristic distance, η is the viscosity and ρ is the density.  (The parameter ν (=η/ρ) is the kinematic viscosity, or momentum diffusivity, which, like all diffusivities, has units of m2 s-1.)  The values of u and L usually relate to solid objects (pipes, obstacles etc) in or around the flow.  For a particle in a fluid, they would normally be the far-field relative velocity and the particle diameter, d.  For powder particles (d ~10-100 μm) in air (η ~ 2 105 Pa s, ρ ~ 1 kg m3, ν ~ 2 105 m2 s-1), the value of Re is likely to be low (<~10), and hence the flow laminar, unless the velocity is quite high (>~10–100 m s-1).

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