46 Canon Moseley on the steady Flow of a Liquid. 



section, inclination, or degree of roughness or smoothness, 



In the case of an open channel 7 = 1. The value of y has 

 been shown to be dependent on that of Uj + Ug*. If U ^ + U2 = 0, 

 •y = I. Now Ug represents the work done by the head of water 

 to overcome the resistances to the motion of the water before it 

 enters the pipe, and Uj represents the work similarly done to 

 accumulate in the water the work with which it leaves the pipe ; 

 if therefore we reason only of that portion of the liquid flowing 

 through an open channel which is at a considerable distance from 

 the point at which it is received into the channel, and which has 

 acquired a uniform and steady state of motion, and if we mea- 

 sure the head of water at any other point below it from this 

 point as its commencement, it is clear that the work U^ is all 

 done by its weight before the liquid enters upon this portion, 

 and also the work Ug ; so that the liquid enters upon this por- 

 tion with no resistance of contraction any longer to be overcome, 

 and no work further to be accumulated in it, but only with the 

 resistances to motion in its channel and motion upon itself as it 

 descends still to be overcome. In respect of that portion of its 

 channel, therefore, Ui + U2=0 and7 = lt. 



Comparison of Theoretical with Experimental Discharge in open 

 Channels of different shapes. 



Assuming 7=1, equations (63) and (65) become 



Mean velocity 



=§-K«)'{-('-f )-}••■ ■ w 



I propose now to test these formulae by comparing them with 

 the important experiments made by MM. Darcy and Bazin on 

 the motion of water in open channels. They made several hun- 

 dred of such experiments in fifty series on channels of difi'erent 

 forms and inclinations and with streams of different depths. 

 The results of the comparison with experiments taken from 

 among these without selection are recorded in the following- 

 Tables. 



* Phil. Mag. November 1871, p. 351. 



f Editor's note. — This is the case alluded to in the Philosophical Magazine 

 for November 1871 as still remaining to be discussed. 



