Desai and Lieber 



where F(s) and G(s) are known functions of s. 



It can be seen from Eq. (2.83) that the cylinder boundary for which s = 

 is a streamline with 0=0. Also the lines of symmetry with 0=0 and 6 = n 

 are streamlines with 0=0. In other words, the streamline 0=0 has branch 

 points at the front and rear stagnation points. Since streamlines are lines for 

 which has constant values, two streamlines having two different constant 

 values cannot meet. Therefore, if a streamline does meet the cylinder bound- 

 ary at any point it must be a branch of the streamline = 0, and the point at 

 which it meets the wall is then a branch point of the streamline 0=0. From 

 Eq. (2.83) we see that can be zero even ii s ^ and e t -n t 0, when the 

 terms in the brackets vanish. This is. 



F(s) 

 G(s) 



(2.84) 



Since |cos e\ < 1, it may happen that there are no points in the flow field which 

 satisfy Eq. (2.84) if the right-hand side of the equation has an absolute value 

 greater than one for all s > 0. Since the value depends on the Reynolds number 

 of the characteristic flow parameter, the existence of a line satisfying Eq.(2.84) 

 also depends on it. 



Let us assume that the Reynolds number is such that a line the points of' 

 which satisfy Eq. (2.84) exists. Then, on this line, 0=0. Since cos d = cos 

 {-6), we conclude that the part of the streamline given by Eq. (2.84) is sym- 

 metric about the polar axis. We may regard it as consisting of two parts, each 

 a mirror image of the other, about the polar axis. In other words, we may say 

 that Eq. (2.84) gives two more branches of the streamline = 0. Denoting the 

 angle i9 at s = on these branches by a, we obtain the angle of separation 



F(0) 

 G(0) 



(2.85) 



If we drop the terms corresponding to the second iteration from the functions 

 F(s) and G(s), and denote the resulting functions by Fi(s) and Gj(s) respec- 

 tively, we obtain separating streamlines due to the first iteration alone from 

 the equation 



cos i9 



Fi(s) 



^T^y ■ (2.86) 



Defining a^ as the corresponding first iteration angle of separation, we obtain 



77 - COS 



Fi(0) 

 Gi(0) 



(2.87) 



574 



