— ; E 



Figure 68 — Streamlines in a channel narrowed 



in a certain manner, as constructed 



with use a line sources. 



See Section 44(D). 



D 



A 





\ 

 / 



C 



B 





\ 



7 



w 



.4' 





/ 



1 } 



\a b 





C D 





\ 

 / 



(a) 



(b) 



Figure 69 - Line source on a rectilinear 

 boundary. See Section 44(E). 



The ratio of contraction or L^/L^ is in all cases a/(a+g). 



If the aj-axis is drawn along the central line of symmetry or y = a/2, then in [44k], 

 [441], and [44m, n] tan~^ is replaced by cot~^, tan by cot, sin by - sin, and cos by - cos. 



If infinite plane walls are inserted along y = and y = a, they form a straight channel 

 with a source in each wall. 



(E) Source Anywhere on Wall of a Rectangular Vessel 



More general cases can be constructed by combining two flows of the type described 

 in this section. Two examples may be noted. 



To represent approximately flow into or out of a small slit at E in the side of a rectan- 

 gular two-dimensional vessel ABCD, as sketched in Figure 69a, flows may be superposed due 

 to two equal rows of sources or sinks perpendicular to the side AA'of an infinite channel, with 

 sources or sinks at E and £"on this side, and a partition may then be inserted along the 

 plane of symmetry BC. 



To represent approximately flow through a small slit located in the bottom of a rectan- 

 gular vessel ABCD but displaced a distance b from the center, combine two rows of equal 

 sources, with the sources 2a apart in each row but the rows differing in position by a - 2b, 

 where a is the width of the vessel, and insert partitions along two consecutive planes of 

 symmetry, such as AB and CD in Figure 69b. 



In both cases, of course, only the flow inside the vessel is represented. (For notation 

 and method; see Section 34; Reference 2, Article 10.4, 10.5; Jaffe'(30); Cisotti (31). 



106 



