Figure 203 - Point source and sini< at ± 

 in a stream. See Section 122. 



' W '2' 



[122d] 



On the a;-axis wherever x > a, r^ = x - a and T2 = x + a; 

 where x < - a, r^ = a - x, r^ = - (a + x). 

 Hence at such points 



u= U - 1 



2a62 \x\ 

 (x^'-a^y 



and (J = \u\. Stagnation points Q^ and Q^ occur where x = - I and I is given by 

 In the plane a; = 0, (7 = jw | , r^ = Tj = \/aj^ + a^, and 



u = - U I 



3/2 



[122e] 



[122f] 



[122g] 



On the a!-axis, \p = Q where a; > a or a; < - a, so that 6^ = 0^' Between x -- a, Q. = n, 

 ?2 = 0, v> = - b'^V. 



The value iIj = occurs also on the surface of revolution S defined by the equation 



a>^ = h^ (cos d^- cos 0j) 



[122h] 



By writing cos 6^ - cos 6^ = (cos^ 0^ - cos^ 0^)/ (cos 9^, + cos 6^) and then expressing 

 cos 0^ and cos ^j ^^ terms of x, ST, and a, the equation can also be put into the form 



309 



