HYDKAULIC POWER TRANSMISSION 715 



Transmission Losses. 



Let p = pressure at pipe inlet in Ibs. per square inch. 

 d = pipe diameter (supposed uniform) in feet. 

 a = area in square feet. 

 / = length of pipe in feet. 

 v = velocity of flow in feet per second. 



144 

 Then the energy at entrance, per Ib. = = 2'31 p ft. Ibs. 



. * . Energy entering pipe per second = II = 2*31 p X 62*4 a v. 



= 144 p a v foot Ibs. 

 144 



= '262 p a v H.P. 1 



f I v z 



Again the loss of energy in friction per Ib. ='^- - foot Ibs. 



2i m 



flv* w 62-4 a v T1 

 /. loss of energy per second = H f = J - X H.P. 



Substituting for v in terms of H we get 



62-4 aH J H }* 

 f ~ 2 m X 550 ( '262 p a ) 



and putting m = - ; g = 32'2 this becomes 



(1) 



l/ 



The energy delivered per second- U 



7^ (fi J 



. * . Efficiency of transmission 



TT 7^2 



(3) 



^d 5 



Differentiating U with respect to H, and equating the result to zero, 

 we get the condition that the maximum horse power may be trans- 

 mitted. 



Expressed algebraically this gives 



H* = ~ 



3 "635 fl ' 1-90/r 



: 



1 If p = 750 Ibs. per square inch we thus get the approximate rule that two gallons of 

 I water per minute is equivalent to one horse power. 



a = -725 , (4) 



