B,29 • TRANSPORT PROCESSES IN FREE TURBULENT FLOW 



U/U<, < 0.2. This means that Dh decreased where Z)„ remained con- 

 stant and decreased more rapidly than Z)„ in the outer regions. 



Corrsin and Uberoi [123] calculated values of Pr^ from their measure- 

 ments in a heated round jet. Their mean values over the cross section of 

 the jet were very close to the value 0.7. They also obtained an indicated 

 increase from the center outward, but did not regard their accuracy as 

 sufficient to be certain of a definite trend. They noted the striking agree- 

 ment with the laminar Prandtl number for air at the mean temperature 

 of the jet. Forstall and Shapiro [124] point out, however, that turbulent 

 Prandtl numbers for jets are about 0.7 for various kinds of fluids irrespec- 

 tive of their laminar Prandtl number. 



Townsend found in his investigations of the plane wake [113] that 

 both Du and I remained nearly constant in the central portion of the 

 wake, but fell off rapidly in the outer part. However, Du divided by the 

 intermittency factor y was not far from constant over the greater part 

 of the wake. 



These pieces of evidence tend to confirm what was conj ectured earlier 

 in this article, namely that insofar as theories based on gradient transfer 

 can be applied at all, they should apply better to momentum than to 

 temperature or concentration. The laminar-type solutions of the equa- 

 tions of motion based on some appropriate constant value of Du over the 

 section have consistently given accurate descriptions of the velocity dis- 

 tribution. Discrepancies occur in the outer part of the flow due to the 

 fact that Du decreases. Townsend has shown that improvement results 

 for the plane wake if the eddy viscosity e^ is allowed to decrease with the 

 intermittency factor, i.e. as 76;^. 



The situation with regard to the diffusion of heat and matter is not so 

 favorable, and transfer based on local gradients is little better than a 

 crude approximation at best. For the round jet, and presumably for the 

 plane jet also, Dh is nowhere constant, but the assumption of constant 

 Prt is beUeved to be acceptable for practical purposes. When Prt is con- 

 stant, the relation between temperature distribution and velocity dis- 

 tribution for the round jet is 



(temperature\ _ /velocity V'"* .„„ 2\ 



ratio / \ ratio / 



While there is some question about the appropriate value of Pr^,, a reason- 

 able value is Pr^ ^ 0.7. 



According to Reichardt [125] Eq, 29-2 should be more generally appH- 

 cable in free turbulent flow. For a review of Reichardt's inductive theory 

 of turbulence, reference is made to [96]. 



For plane wakes it does not seem possible to calculate temperature 

 distribution on the basis of an exchange coefficient for heat. Paradoxi- 

 cally, mixing length theory gives reasonably good agreement with ob- 



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