360 Canon Moseley on the steady Flow of a Liquid. 

 Or neglecting the work accumulated in the efflux, as before, 



wsint 



V = V Q € 2^~ r (37) 



w sin t 

 Since — ^ — =7 is assumed to have the same value for all values 



of i y R remaining the same, it follows that the ratio of the ve- 

 locity of any film to that of the central filament is independent 



w sin l 

 of the slope. Substituting — ^ — for y in equations (16), (28), 



(31), 



^ 3 (2^ 6 K3A2 6 2M , 



2(2^( e ^ R -^R-l)R^ 



Q= i it i .(40) 



e 2^ R—l 



/wsin AfT 



2fi 



^ J L\~ 36R 



If, in equation (38), R= ocfy, 



Q =2 7r(-^-) 2 i; (41) 



This may be considered the limit of the discharge of a pipe, of 

 however great diameter, which is placed on a given slope, and 

 whose central filament is made to move with a given velocity v . 



The horse-power lost by water inflowing through a pipe. 



The work lost by a liquid in flowing through a pipe is, 1st, 

 that represented by U 3 *, which is expended on the resistance to 

 its flow by the internal surface of the pipe ; and secondly, that, 

 U 4 *, expended internally on the resistances opposed to the flow- 

 ing of the films over one another. The whole work so lost is 

 therefore represented by U 3 -fU 4 . Now, by equation (5), 



U 3 = 27rR/(^ ] + X 1 V 2 )V; 



or, neglecting fi } as small in comparison with XjV 2 , 



U 3 =2tt/X 1 RV 3 . 



* Phil. Mag. September 18/1, p. 186. 



