Therefore at the edge of the boundary layer equation (3-5) will take 

 the form 



dUcQ - _ 1 dP 



at p ax 



(3-12a) 



Subtracting now (3-12a) from the complete boundary layer equation 

 (3-1) we obtain 



9H +U 9H +V ^= ^2 +v ^f (3-13) 



at ax ay at a y 



The value of u and v is zero at the wall and equal to U<x> and Vg, respect- 

 ively at distance 6 from it, where 6 = /— ; within the boundary layer, 



V 03 

 therefore to the first approximation tulljU oo | . Moreover it is reasonable 



to asume that in the same region 



1 



t 2 - = k 



ay 6 ax 



From continuity then V - 5k Uoo 



Let us now examine the order of magnitude of the terms in equation 

 (3-13) 



au . au m _ 2 



au 2 2 , , 2. 



u ^ — = Uoo k Um = k a ti) = ka (ao) ) 



ax 



V 



au 



ay 



V 



a 2 u 4 

 ay 2 



o 2 



= §k UooUoo/5 = k Uoo = ka (auj ) 



Uoo UooU) ? 



' §2 = V ~J~ ~ Ubbus = auu^ 



So we see that the quadratic terms are smaller than the rest by a factor 

 ka and since according to our basic assumption ka « 1 these terms can be 

 omitted. 



The boundary layer equation (3-1) to a first approximation may be 

 written now as 



*H = BJk + v sL" ( 3 -13a) 



at at ay 



