188 UNIFORM PIPE CONNECTING TWO RESERVOIRS. 



& 



loss of work due to the resistance at ingress = 0W; (3) 



y 



V* 



work stored in the water at discharge =. W. (4) 



104. Uniform Pipe connecting Two Reservoirs, 

 when all the Resistances are Considered. Let h be 



the difference of level of the reservoirs, and v the velocity, 

 in a pipe of length I and diameter d. Then we have 



work due to the head of water = h W, (1) 



which is the whole work done per second in moving W 

 pounds of water from the surface of one reservoir to the 

 surface of the other. This work is equal to the work in 

 overcoming all the resistances, together with the work re- 

 maining in the water at discharge. That is, the work is 



V* 



expended in three ways: (1) The head ,* corresponding 



*9 



to an expenditure of W foot-pounds of work, is employed 



in giving energy of motion to the water, and is ultimately 

 wasted in eddying motions in the lower reservoir. (2) A 



v* 

 portion of head ft =- , corresponding to an expenditure of 



v* 

 fttr-W foot-pounds of work, is employed in overcoming the 



. 

 resistance at the entrance to the pipe. (3) the head f 



f-jn- > corresponding to an expenditure of f-jn~W foot- 



pounds of work, is employed in overcoming the surface 

 friction of the pipe. Hence, from (1), and (2), (3), (4) of 

 Art. 103, we have 



Culled velocity head. t Called/ric/ion head. 



