B • TURBULENT FLOW 

 Karman hypothesis [47], 



0.242 



vc;, 



= log (CfMe) 



Prandtl hypothesis [48], 



Cf, = 0.472(log i2e)-2-68 



(12-17) 



(12-18) 



As an additional comparison, the power law of Falkner according to Eq. 

 13-5 with A = 0.0262, n = y is also plotted, and agrees well with the 



c, 



Fig. B,12b. Compressibility effect on skin friction 

 (theories), after Chapman and Kester [29]. 



Kdrmdn and Prandtl hypotheses. The Prandtl law has originally the coef- 

 ficient 0.472 but Schlichting adopts a coefficient 0.455. Eq. 12-17 is some- 

 times called the Kdrmd,n-Schoenherr formula, and Eq. 12-18 the Prandtl- 

 Schlichting formula. 



Although the skin friction coefficient at low speeds does not depend 

 very much on the Karman or Prandtl hypotheses, with the application 

 of those hypotheses to high speeds there arise many uncertainties. Now 

 consideration must be given to new exchanges, such as density mixing 

 and heat transfer, and to the variation of fluid properties across the 

 boundary layer. An investigation of the theoretical basis of skin friction 

 as given above will reveal many passages which are uncertain and arbi- 



( 112 ) 



