17 



A general equation for the variation of the skin friction in a pres- 

 sure gradient will now be derived from the law of the wall by using the power- 

 law formula for the velocity profile of the inner flow, 



k - -&T 



[30] 



As before, at y = 6 , u = u and 



u 0\»O 



u T \ v I 



!31] 



After substituting u, 



V? 



and y = T7 » there results 



pU 2 [ e i 



[36] 



For two different pressure gradients at the same Reynolds number R and conse- 

 quently at the same value of C and n , 

 the following ratio can be formed 



/ W \ r 2 



ipU 2 "^ 



[37] 



If the reference condition is that 

 for zero pressure gradient, this 

 equation becomes 



pU pU o 



[38: 



where the subscript zero refers to 

 zero pressure gradient. For a power- 

 law velocity profile of a flat plate 

 with zero pressure gradient, Equation 

 [14] becomes 



H - 1 

 n o = -^— [39] 



T 



c o 



r - /71 f rrn nv n >>))>)>))) n )>> )/ n 



to 



e >» 

 = O 



SI 



Figure 7 - Regions of Flow Within the 



Turbulent Boundary Layer in a 



Pressure Gradient 



