Dynamic eddy kinematic

A brief derivation of the turbulent velocity profile for Newtonian fluids in smooth pipes will first be presented and then extended to power-law fluids. The shear stress at any point in the fluid, at a distance y Irom the wall, is made up of viscous and turbulent contributions, the magnitudes of which vary with distance irom the wall. Expressing shear stress in terms of a dynamic viscosity and an eddy momentum diflnsivity (or eddy kinematic viscosity), E,... 

Kinematic and geometric similarity in fluids ensures geometrically similar streamline boundary films and eddy systems. If forces of the same kind act upon corresponding particles at corresponding times, they are termed corresponding forces, and conditions for dynamic similarity are met. While the scale-up of power consumption by a unit operation or manufacturing process is a direct consequence of dynamic similarity, mass and heat transfer—direct functions of kinematic similarity—are only indirect functions of dynamic similarity. 

Although these eddy diffusivities act in the same manner as the kinematic viscosity and thermal diffusivity in laminar flow, the critical difference is that the eddy diffusivities are not properties of the fluid but are dependent largely on the dynamic behavior of the fluid motion. In this section the fluid dynamic bases for evaluating these eddy diffusivities are given. They will then be used in a variety of convective heating situations to yield formulas useful in engineering computations. 

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