716 HYDRAULICS AND ITS APPLICATIONS 



from which, by substitution in equation (2), we have the energy delivered 



through the pipe, or U = '483 >/ y^ H.P. 



= 138 y/ 





of h = head in feet at entrance to pipe. 



Substituting the value of H from (4) in equation (3), we see that under 

 circumstances of maximum transmission, the efficiency is , and that J of 

 the energy entering the pipe is absorbed in overcoming friction. On the 

 other hand it is evident that maximum efficiency is obtained when H is 

 as small, and p and d as large as practicable. 



The point at which it ceases to pay to still further increase the diameter 

 of the pipe line for a given horse power, depends on the relative cost per 

 yard of the pipe line, including excavation, jointing and laying, and of 

 the power production per horse power. 1 In general, however, a size of 

 pipe which allows of a pressure drop of about 10 Ibs. per square inch per 

 mile will be found to give most economical results in practice. In modern 

 practice the largest pipes are about 6 inches diameter, the pipe lines i 

 being duplicated for large powers. 



EXAMPLE. 

 Let H = 100 H.P. 



p = 750 Ibs. per square inch. 

 Assume /= *006 (this varies with the diameter, velocity of flow, and 



condition of pipe). 

 Then allowing for a drop of 10 Ibs. per mile we have 



Efficiency of transmission = 1 =^ 



= 1- 



750 5,280 



635 / 1 H 2 



A d 5 ' 



75 - '635 X -006 X 5,280 X 10,000 X 750 . 



750 X 750 X 750 X 10 

 = '0358 feet, 

 .. d = -514 feet = 6'17 inches. 



The loss per mile H f = ^ X 100 = 1-88 H.P. 



J See " Proceedings Institute Mechanical Engineers," 1895, p. 353 ; also Engineering, 

 May 22nd and June 5th, 1891. 



1 



