point on the cylinder, divides, passes around it, and then continues along the extension of 

 PO. The extension of OP to the right of P is the streamline for xjj = 0. 

 The velocity potential is, from Equation [40b], 



,^=-4 log (-^) , [51b] 



or, in a dimensionally balanced form, 



<^ = -4 1og(-^) [51c] 



where r^, r,, and r are distances as shown in Figure 78. The complex potential, with the 

 origin on the axis of the cylinder and the source at (A,,0), is 



w ^ -A I log (s - Aj) + log (s - h^) - log 3 



The components of velocity may be written down from Equations [40e,f]. 

 On the cylinder, taking ds = a d 6, 



[51d] 



q = --^= ^= 4 — +— sin e 



ds a dd \ rf 2 J 



T^ = a? + A 2 _ 2^^^ pQg Q^ ^2 = ^2 ^ j^2 _ 2ah^ cos d , 

 or, using the similar triangles again to show that '"o/'"! = a/A^, 



q = 2A — sin e. [51e] 



Half of the flow net, which is symmetrical with respect to tho OP axis, is shown for 

 A^ = 2a in Figure 79. The source is at P. 



The total force per unit length on the cylinder is 



^^^upa^A^ [51f] 



A^ (hf - a^> 



and is directed toward the source. This result is easily obtained from the Blasius theorem 

 and the residues at s = and z = A,; compare Section 42. 



118 



