111. EFFLUX FROM A TWO-DIMENSIONAL ORIFICE. 



Consider the steady irrotational outflow of a liquid through a parallel-sided slot of 

 width 2a in the infinite plane wall of a tank. Let gravity be assumed not to act. In Section 61 

 the problem was solved on the assumption that the liquid remains in contact with the outer 

 face of the wall. It will now be assumed that the issuing liquid separates from the wall in the 

 form of a jet bounded on each side by free streamlines. 



On the 3-plane let the slot be represented by the segment (-a, 0) to (a, 0) of the real 

 axis, as in Figure 179; and, for simplicity, let the constant velocity along the free streamlines 

 be q = 1. 



I 



J 



(3 = -i~) 



s: r 



£ B^ g A 



~~1 ^"^\ \7o Ji Z^ 



(C.C.'J) 



JnC 



(a =1/2) 



5 











1 









{c,c:j) 











f 





1 





(o.= l/2) 



B' 







iCC'J) B' 



1 



Figure 179 — Efflux from a two-dimensional orifice. See Section 111. 



As explained in the last section, the motion is first studied in terms of the variable 



c = 



dw 



[Ilia] 



272 



