354 Canon Moseley on the steady Flow of a Liquid. 



formly through a circular pipe. The sections of the coaxial films 

 are shown by the parallel lines in the figure, and the parts of 

 these lines included in the space C D c represent those portions 

 of the films which would have fallen off from the pipe in one 

 unit of time if they had not moved on (as they are here supposed to 

 do) in the same directions and with the same velocities after they 

 had passed the end of the pipe as they had when they came to it. 



Also let C B b c be the space which on the same supposition 

 would have been filled with liquid in one unit of time if there 

 had been no resistance of the internal surface of the pipe, and 

 therefore no differences in the velocities of the films ; and, lastly, 

 let Ada be the space which would be left vacant in a unit of 

 time at the upper end of the pipe if none were admitted there, 

 and the surrounding liquid did not flow into the vacancy. The 

 resistance of the internal surface of the pipe — 



1st. Stops back in every unit of time as much of the liquid as 

 would fill the space BCD cb, and therefore destroys as much of 

 the work which would otherwise be done by the weight of the 

 liquid in each unit of time as is represented by h multiplied by 

 the weight of the liquid so stopped back. 



2ndly. It causes the coaxial films of liquid to slip over one 

 another, which otherwise they would not, and thus it creates the 

 resistances of these in their motions over one another, and de- 

 stroys as much of the work which would otherwise be done by 

 the weight of the liquid effluent per unit of time as is represented 

 by the aggregate work of those resistances. 



Taking, therefore, U 3 to represent the work per unit of time 

 of the resistance of the internal surface of the pipe, as before*, 

 and U 4 to represent the aggregate of the works per unit of time 

 of the resistances of the films in moving over one another, 



U 3 = (weight of liquid which would fill the space B C D c b)h + U 4 . 



But 



(weight BCD cb)h= (weight B C cb)h- (weight C c~D)h; 



.-. U 3 = (weight BCcb)h- (weight CcD)£ + U 4 . 

 But 



(weight BC cb)h— work which would be done by weight of 

 efflux per unit of time if there were no resist- 

 ance, 



„ „ =?(;7rll 2 i>t. 



* See Phil. Mag. September 1871, p. 186. 



f See Phil. Mag. September 1871, p. 188, equation (8). 



