HYDRAULIC GRADIENT 



247 



considered, the ends of all such ordinates being connected give a curve 

 called the hydraulic gradient for the pipe line. If now any datum 

 line C D be taken, such that tha height C A represents the potential 

 energy of the water at A, the height of any point on the gradient line, 

 above G D, will evidently represent the head available for producing flow 

 at that point, while the pressure energy at all points on the hydraulic 

 gradient will be zero. It follows that if a series of open stand pipes 

 are erected at various points on the pipe line the free surfaces in these 

 pipes will lie on the gradient line, while the pressure in the pipe at any 



Fricttonal Loss in Pipe- 



toys due to Sudden Enlargement _L 



FIG. 110. Hydraulic Gradient. 



point will be measured by the vertical distance y it yz, etc.. of that point 

 below the gradient. 



The slope of the hydraulic gradient is termed the " virtual slope " 

 of the pipe. 



Fig. 110 represents the hydraulic gradient for the pipe line shown 

 in elevation, which consists of a parallel pipe P Q, having a sudden 

 enlargement of section at Q, remaining parallel from Q to R, and dis- 

 charging at R into the service reservoir E. 



Here a b represents frictional and eddy loss at entrance : b d repre- 



sents frictional loss from P to Q = 



fhv? 

 2 g mi 



ft.-lbs. per Ib. : d e represents 



loss due to sudden enlargement of section = - ft.-lbs. per Ib. : 



* 9 



2 



e' f represents loss due to friction between Q and R = ~ - ft.-lbs. 

 per Ib. : f k represents loss due to rejection of kinetic energy at exit. 



