230 VARIABLE MOTJOtf. 



the mean of these results will give the friction head approx- 

 imately. Therefore, taking the mean of (7) and (8), and 

 substituting for a its value from (4), we have, for the re- 

 sistance of friction, 



Ip __ Ip 1 



- 



[from (5)]. 



Substituting (6) and (9) in (3), we have, for the whole 

 head, 



Solving (10) for Q, we have 

 K 



Q= 



Vi 2 V 



In a prismoidal channel it will be a sufficiently close ap- 

 proximation to the truth to assume that the surface line of 

 the water is straight, and then from this assumption to com- 

 pute the transverse sections and their perimeters. When 

 we have these, with the quantity of water carried and the 

 length of a portion of the river or canal, we may determine 

 the corresponding fall li by (10) ; and when we have the 

 length, fall, and cross-section, we may determine the quan- 

 tity Q by means of (11). Where greater accuracy is re- 

 quired, we should calculate h or Q for several small portions 

 of the stream, and then take the arithmetic mean of the 

 results. If only the total fall is known, this value should 



be substituted for h in (11), and instead of g ^ we 



