Estimation of the Turbulent Eddy Viscosity

We now turn our attention to the estimation of the ratio z turb/ - The starting point for our analysis is the equation of motion, which for steady-state conditions gives the shear stress profile as (see, e.g.. Bird et al., 1960) 

Transforming to the y-coordinate system and introducing the constitutive relations for the shear stresses due to the molecular contribution (r = — /jl du/dy) and due to the turbulent eddy contribution = — Mtu.b du/dy) we can write Eq. 10.2.11 in terms of reduced parameters as follows  

The ratio y /R is negligibly small for problems in which the major concern is the estimation of heat and mass transfer rates. This can be seen from the fact that most of the resistance to mass and heat transfer is concentrated in a thin zone of thickness y = 5. The term has a value exceeding 300 for Re = 10,000. We shall, therefore, approximate the term (1 - y /R ) by unity in the ensuing analysis. With the right-hand side of Eq. 10.2.12 set to unity we may rewrite it as 

This ratio can be estimated if the functional form u y ) is known. 

The von Karman velocity profile for turbulent flow is given by three equations. 

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