sources predominate, so that fluid must be carried away on the whole, or in the opposite 

 direction if sinks predominate. 



Figure 208 — Diagram for a source at and 



a compensating line of sinks, in a 



stream. See Section 125. 



As a further example, suppose that sinks are distributed continuously and uniformly 

 along the j;-axis from - a to and that there is also a single source at the origin of strength 

 numerically equal to the total strength of the sinks, together with a superposed uniform flow 

 at velocity [/ toward negative x\ see Figure 208. 



Let - in- a denote the volume of fluid absorbed by the sinks on unit length of the 

 axis; a is thus a negative number and represents algebraically the source density on the axis. 

 Then, if the volume emitted per second by the single source is 47r.4, 4n-/l = - i/raa and 



[125a] 



The total potential (jS and stream function i/i"at any point P or {x^lS), where cu denotes 

 distance from the a;-axis, can be written, from [119a,b,d,f] and [123d, e], 



^ = V 



r.+x + a.-, 



\t a r + j; /J [ \r a r + r -a /J 



4, = V 



.2 \r a I \ 12 



2ar 



[125c] 



where b^ = A/U and t , r are the distances of P from the two ends of the line of sinks or, as 

 illustrated in Figure 208, 



315 



