Figure 204 - Streamlines past a rankine solid of revolution, obtained from 

 source and sink at - a. 



ads 



[123a] 



where r denotes distance from ds to (x,t/, z) and the integral is to be extended over the entire 

 curve. Both a and r may vary along the curve. 



The uniform line distribution. As an importaht special case, let a be uniform along 

 the j;-axis from x = a to x = b. In the integral for (^ write dx' for ds and x' for the value 

 of x at ds. Then 



cj) = a 



dx' 

 ■~J~ » '■'= [(x- x')^ + 



[123b,c] 



where w denotes distance from the a;-axis. In this case an antisymmetric stream function i/( 

 also exists; integration of [119f] gives for it 



■f 



dx' 



See Figure 205. 



Evaluation of the integrals gives 



= 6 



<^ = - a In { [(j;' - a;)^ +75^] -{x'-x)\ 



311 



