.91 93.] FLOW FROM A CANAL. 97 



cannot be realized, for the reasons explained in Art. 30. If how 

 ever the motion be very slow, we may take two stream-lines very 

 near to ^r = TT as fixed boundaries, and so obtain a possible case. 



93. Example 9. Kirchhoff has, d propos of certain problems 

 to be discussed below, given a method by which the determination 

 of the motion in several cases of interest may be readily effected. 

 The method rests upon the property of the function f explained 

 in Art. 90. If the boundaries of the fluid be fixed and rectilinear, 

 the corresponding lines in the plane of f, which are also straight, 

 are easily laid down. Also, since the fixed boundaries are stream 

 lines, the corresponding lines in the plane of w are straight lines 

 TJr = const. It is then in many cases not difficult to frame an 

 assumption of the form 



by which the correspondence of these lines in the planes of f and 

 w may be established. The relation between z and w is then to 

 be found by integration. 



Example 8, above, is very easily treated in this manner. We 

 take however a somewhat less simple case ; viz. that in which a 

 current flows from a uniform canal into an open space which is 

 bounded by an infinite plane perpendicular to the length of the 

 canal, and in which the mouth of the latter lies. See Fig. 6. 



Fig. 6. 

 Y 



The middle line of the canal is evidently a stream-line ; say 

 that for which = 0. Also for the stream-line BAC let &amp;gt;r = 7r; 



L. 



