MOTION OF WATER IN PIPES. 187 



ered by this pipe will be d? times that delivered by the for- 

 mer, therefore for the same quantity of water delivered as 

 by the former, the resistance of friction in the latter pipe 

 will be 



fid ,, I 



~w fv 



that is, the resistance of friction in pipes, when the ve- 

 locity is constant, varies directly as their lengths and 

 inversely as their diameters. 



If we measure this resistance by a column of water, and 

 denote the height of this column by h lt we have 



where/ is a constant to be determined by experiment, and 

 is called the coefficient of friction. 



This height h^ is called the height of resistance of friction, 

 which has to be subtracted from the total head 7^, in order 

 to obtain the height necessary to produce the velocity v. 

 Hence, the loss of head or of pressure, in consequence of 

 the friction of the water in the pipe, is found by multiply- 



ing the head due to the velocity by the coefficient f-., and 



is greater, the greater the ratio of the length to the diam- 

 eter and the greater the height due to the velocity. 



Multiplying (1) by W, we obtain for the work due to the 

 resistance of friction 



that is, the loss of work by friction is the same as that 

 of raising the water through a height A,. 



COH- From (4) of Art. 96, we have 



