300 . HYDRAULICS AND ITS APPLICATIONS 



For maximum value /~ ; 2 b d 

 of Q \ 



(1 + s 2 ) d 2 = (b + 8 d)' 2 (2) 



But from the figure it will be seen that if a circle having its centre in 



K 50 - __* the surface of the water can be 



\ m _g | |/ drawn to touch the sides and 



bottom, we have 

 . m n = b -f- s d ; m p = in q 

 = s d ; n p = d, 

 and since (m n) 2 = (w jo) 2 -}- 

 (?i_p) 2 , the above equation is 

 satisfied. These proportions 

 then give the best results. 



The value of s depends large- 

 ly on the material in which the 

 channel is excavated. The following may be taken as the minimum 

 permissible values. 



Earthen canal with faced sides s = TO. 



natural s = T5. 



,, in light soil s = 2'0- 



The latter value is usually adopted for all unfaced earthern sides. 

 Substituting this value of s in equation (2) we have 



5 d 2 = (b + 2d) 2 



/. d = 4'24 b (3) 



/. For maximum discharge d = 2*12 B, where B is the bottom breadth. 



FIG. 129. 



We then have 



g = cVp-.i 



_ c / (aftd 

 ' 2 (b + d 

 Substituting for d from (2) we have 



<P) ! 



and giving s the value 2 



Q = 204 (7 /^ cub. ft. per sec. 

 if C and i are taken in foot units 



Q = 36-1 C B*. 



Qr 



