For a linear velocity profile, [24], 



= A [281 



6 



where 9 is the two-dimensional momentum thickness 



•f^i'-f)' 



.8 



^H 77(1- 77- Wy [29] 



■'0 



Substituting d in [27] gives 



dx 

 Integrating the linear differential equation, [30], produces 



+ i.^(r eV^^"-^ [301 



('■-'^^ -if.]' '-'"'" 



[31] 



with the stagnation point aj = as the initial point of integration. An interesting feature of 

 this result is its being identical in both form and numerical constants to the semi-empirical 

 result of Thwaites^ when his two-dimensional solution is extended to the axisymmetric 

 case.^° Thwaites averaged known solutions of two-dimensional laminar boundary layers for 

 a variety of pressure gradients. 



Now the momentum area 12 for axisymmetric boundary-layer flow in general may be de- 

 fined as 



Q = I ".(l- «.\r<iy [32] 



Since 



with 



then in general 



T = T +y cose [11] 



0<y<S 

 - cosa-1 



[33] 



'■«; ^ < " < ('-.^ + 5) ^ [34] 



Hence for 5 « t^ which is the case under consideration 



fl = r... 6 [35] 



