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Reynolds number is defined as follows:

Re = &rho * U * D / &mu

where &rho is the specific gravity of the fluid, U -- it's velocity, D -- the diamater of flow, and &mu -- the viscosity.

Reynolds found that when a fluid flow is associated with a Re of under 2100, the flow is laminar. If it is associated with a Re > 4000, the flow is turbulent. And in between -- borderline.

No clear theoretical basis for this observation, but it has been borne out for various values of &rho, U, D, and &mu, and various fluids.

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