248 HYDRAULICS AND ITS APPLICATIONS 



The vertical distance from the datum to the broken line a b d cfk, 

 now represents the sum of the (kinetic + pressure + potential) energies 

 at any point, and if c g be drawn parallel to b d at a vertical distance b c 



a 



below b d, equal to ^-, the distance from the datum to the line c g 



* 9 



now gives the sum of the (pressure + potential) energies at any point 

 from P to Q, If similarly a line h k be drawn parallel to ef, at a vertical 



a 



distance below this equal to ^-' the whole line a b c g h k now repre- 

 sents the hydraulic gradient for the pipe. 



The pressure in the pipe line will be everywhere greater than that of 

 the atmosphere, so long as the pipes nowhere rise above the hydraulic 

 gradient. If part of the pipe line be laid above the gradient line, the 

 pressure in this portion of the pipe will be less than atmospheric, and 

 any leakage at a joint allows air to be drawn in with a possible stoppage 

 of flow. If the pipe rises above the gradient line by a distance 

 equivalent to the barometric height, 34 feet, the flow will of necessity 

 stop completely. Owing to the discharge of dissolved air from water at 

 low pressures, the maximum height practically attainable is however 

 much less than this. The syphon (Art. 82) is an instance of the pipe 

 line being above the hydraulic gradient. 



If then the suffixes A and E refer to the surfaces in the two reservoirs 

 and if Z A and Z E are the heights of these free surfaces above some datum, 

 we have, if the pipe discharges below the surface in the lower reservoir 

 ZA ~~ ZE = A^LE = losses at entrance + losses in pipe 

 -f- losses at exit. 



ART. 72. DETAILED LOSSES IN PIPE LINE. 



(1) Losses at Entrance. These depend on the form of entrance 



v 2 

 adopted. Thus with a bell mouthpiece the loss of head is about *05 ^ 



feet of water (p. 119), while with a pipe projecting into the reservoir 

 and forming a re-entrant mouthpiece, the loss, when running full, is 



v* 



~ feet of water (p. 118). 

 ^ 9 



Where the pipe opens flush with the side or bottom of the reservoir 



v 2 

 the loss of head becomes about *47 ~ feet (p. 117). 



^ ff 



From what has already been said, it will be seen that this loss of 

 energy occurs simply in getting the water into the pipe, due to the 



