HYDRAULICS 375 



h 

 however, be used. The table gives, for that pipe, -= .012, and 



therefore, A = 3,OOOX.012 = 36 ft. The piezometric elevation 

 at the junction Os is, then, 517 36 = 481. Proceeding as 

 before, it is found that each of the branches F and G requires 

 an 8-in. pipe. 



Assuming an effective head of 30 ft. for L, the value of 



- is 30 -T- 2,000 = .015, and the pipe L is found to be between 

 an 8- and a 10-in. pipe. For the 10-in. pipe, and the delivery 

 of 2 cu. ft. per sec., the value of - is .0057; therefore, h = .0057 



X2,000=11.4 and the piezometric elevation at Ot is 481.0 

 11.4 = 469.6. The branches / and Hare found to require 

 diameters of 8 and 6 in., respectively. 



HYDRAULIC GRADE LINE 



The hydraulic grade line, or hydraulic gradient, is a line drawn 

 through a series of points to which water would rise in piezo- 

 meter tubes attached to a pipe through which water flows. 

 With a straight smooth pipe of uniform cross-section, the 

 hydraulic grade line is a straight line extending from the 

 reservoir to the end of the pipe. 



In the accompanying illustration is shown a horizontal pipe 

 leading from a reservoir to a stop-valve 5. When the valve is 

 open so that water from the pipe discharges freely into the 

 atmosphere, the hydraulic grade line is the line adfg. The 

 distance of the point a below the surface of the water in 

 the reservoir represents the head absorbed in overcoming the 

 resistances of entrance to the pipe, and in producing the veloc- 

 ity with which the water flows. In the same way, the differ- 

 ence in the height to which the water rises in any two 

 piezometer tubes represents the head absorbed in overcoming 

 the resistance to flow in the pipe between the points at which 

 the tubes are inserted. 



The flow of water through the pipe P would be the same 

 whether the pipe were horizontal, as shown in the illustration, 

 or whether it were laid along the grade line adfg. The flow 



