B • TURBULENT FLOW 



pointed out earlier by Clauser about the law of the wall, this feature now 

 has a simple explanation. If we regard the phenomenon as a sharp drop in 

 velocity to zero at the wall instead of a rise from the wall outward, we see 

 that this is simply the region where wall friction becomes predominant 

 over the pressure effect. In other words, this is the region governed by 

 the law of the wall. Typical of the agreement with the law of the wall 

 and of the manner of departing from it are the examples shown in Fig. 

 B,19b taken from Coles' paper [85]. When the Reynolds number is high 

 and the pressure is either constant or the adverse gradients are not exces- 

 sive, the agreement is more as shown in Fig. B,19c given by Clauser [55]. 





1 



10 



100 1000 10,000 100.000 



U.y/v 



Fig. B,19b. Agreement and departures from the law of the wall, after Coles [55]. 



The region of the wall is a region for which we have a unique relation- 

 ship between the velocity and the shear stress at the wall. Sometimes, 

 slightly different working formulas evolve from the fitting to experimental 

 data. We find, for example: 



According to Clauser y^ = 5.6 log 



According to Coles 





5.75 log (^) 



+ 4.9 



(19-1) 



+ 5.10 (19-2) 



It is difficult to specify where departures from the law occur, because 

 this depends both on the Reynolds number and the pressure gradient. 

 Departures occur at lower values of UrV/v and are greater as the effect of 



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