21 



ferential form of the momentum equation for axisymmetric turbulent boundary layers on bodies 

 of revolution 



^ + (A + 2) il 1^ = r 

 dx ^ ' U dx " 



pt/2 pV^ dx J 



where the momentum area Q is defined in Equation [32]. In terms of the displacement area A* 

 defined in [10] and Q, the shape parameter for axisymmetric flow is 



h =^ 



[62] 



The momentum equation, [61], will now be considered for the two cases where the boundary 

 layer is thin compared to the radius of the body and where the boundary layer is of like 

 magnitude. 



BOUNDARY LAYER THIN RELATIVE TO BODY RADIUS: S « r^ 



In the region forward of the tail, the boundary layer is thin relative to the radius of the 

 body 8 «T^. Here the momentum equation, [61], may be reduced to a simpler form. 

 Since within the boundary layer 



it follows from [32] that 



from [10] that 



'u;^ < " < (^. + 5) 



'w^*< A*< ('•.„ + 5) S' 



and from [62] 



where H is the two-dimensional shape parameter 



Also 



d 



o d o 







Evidently for 5 « r^ , fi = r^ 6, K* = T^d*, h = H, and 



.8 .S 



[63] 



[34] 



[64] 

 [65] 



[66] 



[67] 



i J "'^'ii'- I -'y) 



