290 "HYDRAULICS AND ITS APPLICATIONS 



If A sectional area of channel beneath water line, and if we assume 

 the resistance to be equally divided over the area we have, if p = resist- 

 ance per unit area of the stream 



Here -p or m is the hydraulic mean depth of the section. 



If the channel be of uniform slope -j , where -=- = i = sin (0 being the 



angle of inclination), then the weight of water in this length I, per unit 

 area of the channel, being W I Ibs., the resolved part of this weight in 



the direction of motion = W I -j- = W h Ibs. 



.*. If the velocity is constant so that this force is entirely expended in 

 overcoming friction and not in producing acceleration, we have 



f" I v 

 li ' 



m 



, jlv n 

 or h =fr- 



2 g m 



In an open channel n may be taken as being approximately equal to 2, 

 so that the formula becomes 



This may be written in the form adopted by -Chezy, viz., 



*A * m = c V^Ti (2) 



/ * 



where ^ = T 



Many experiments have been devoted to determining the values of C 

 or of / for channels having different physical characteristics, and the 

 results of the more important of these are as follow, the numerical 

 values of the coefficients obtained by the various observers being collected 

 and tabulated on pp. 293297. 



Darcy and Bazin (1855 9), as the results of experiments carried out 



on the Bourgoyne Canal, gave C the value , where a and b 



Ya + A 

 m, 



(p. 293) vary only with the material and condition of the bed qncl sides 

 of the channel. 



