Flow from a Disturbed Area. 

 The under-body will be as in fig. 4. 



Fisr. 4. 



tut/asaa 



jLr£ ag 



449 



Velocity at infinity, # = ^~ c . 



Velocity at B, 



7» = /7 « * 



VIII. Flow through a semi-infinite pipe. 



It has been pointed out in para. II. that the disturbed motion 

 of a free surface leads to consideration of a function having 

 an essential singularity. 



Let 



dz 



y — Z — , 3 -iesin/3£ 1/2 



3 Jr... c '— 



dw 



— w =log(l+^. 

 — co <w<0, i.e. co >f>(). 

 dz 



v/, 



/,-iesinj8 \t 



(16) 



a free surface over which lies between +c. 

 It is of semi-infinite extent since 



7/F - IT; 



$\d:\ — >co. 

 0<w<+co, i.e. 0>/>— 1. 



# = and (j goes from 1 to g-csini^ 



and £■ — ->—co along a rigid boundary. 



Phil. Mag, S. 6. Vol. 38. No. 226. 0c«. 1919. 2 I 



