Newtonian fluids, mixing theory

Equation (6-37) represents the friction factor for Newtonian fluids in smooth tubes quite well over a range of Reynolds numbers from about 5000 to 105. The Prandtl mixing length theory and the von Karman and Blasius equations are referred to as semiempirical models. That is, even though these models result from a process of logical reasoning, the results cannot be deduced solely from first principles, because they require the introduction of certain parameters that can be evaluated only experimentally. 

A relatively simple correlation for mixing time in bubble columns with non-Newtonian fluids was proposed by Kawase and Moo-Young [32] using the isotropic turbulence theory as follows... 

A. B. Metzner, Non-Newtonian Technology Fluid Mechanics, Mixing, and Heat Transfer R. Byron Bird, Theory of Diffusion... 

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