B • TURBULENT FLOW 



ally be small and scarcely outside the usual random scattering due to 

 observational errors. 



The function g is affected to degrees that are far from negligible by 

 conditions imposed on the flow from without. The effect of the pressure 

 gradient, which will be considered in Art. 19, is of most importance. It is 

 also affected by free stream turbulence and is therefore different in pipes 

 and channels than in boundary layers. This sensitivity of the velocity- 

 defect law to outer conditions stands in sharp contrast to the law of the 

 wall which is remarkably insensitive in this respect. 







I 



3 



D -10 



-20 



0.2 



0.4 



0.6 



0.8 



1.0 



y/5 



Fig. B,16. Data for smooth and rough walls plotted on basis of velocity-defect 

 law. (Taken from Clauser [72] omitting data source and designation.) 



B,17. Logarithmic Formulas. From time to time it has been 

 inferred in the literature that the two laws, Eq. 16-1 and 16-3, are em- 

 pirical laws, and in the sense that their adoption has depended on experi- 

 mental confirmation, they are empirical. Certainly they draw but little 

 on any knowledge of turbulent structure. About their only connection 

 with the behavior of turbulence is the justification of the assumption that 

 transfer processes are affected by viscosity very near a wall, but are inde- 

 pendent of viscosity and dependent on the scale of the shear layer in the 

 bulk of the flow. The principal empirical fact about these laws is that 

 their regions of validity overlap one another. There is nothing in their 

 makeup that requires an overlap, and the only apparent reason for it is a 

 gradual change from wall conditions to outer-flow conditions. 



Millikan [73] has shown that if there is any region of overlap, no 

 matter how limited, in which both laws are valid, then the functions 

 / and g must be logarithms. Since this is the same form which results 

 from mixing length considerations, but which is arrived at without re- 



< 124) 



