74 HYDRAULICS AND ITS APPLICATIONS 



of its elasticity, and would be given out during expansion. If, in the 

 cylinder in question, the piston were fixed, and the water allowed to escape 

 through a small nozzle, the kinetic energy of the issuing jet would equal 

 the ahove expression, while the pressure would, with the removal of the 

 first few drops of water, fall to that of the atmosphere. 



The amount of energy thus stored in the water per Ib. in virtue of its 



7> 2 

 elasticity is ~ * w foot Ibs., and if water were a perfectly incompressible 



fluid, so that K = oo, would be zero. But this is not what is meant in 

 hydraulics by the pressure energy of water. 



Suppose, however, the piston pressed home with a continuous pressure 

 of p Ibs. per square foot, while the water escapes from the cylinder. The 

 work done on the water per cubic foot is now p foot Ibs., and per Ib. 



is , foot -Ibs. 



The pressure of the water is exactly the same as before, but now, so 

 long as the piston is moving, the water is capable of doing work, in 



virtue of this pressure, at the rate of ~ foot Ibs. per Ib., and this is what 



is meant by the pressure energy. 



The idea of pressure energy only becomes applicable when we have a 

 continuous supply of water under pressure, as is the case, for example, in 

 the supply pipes of an hydraulic power company. Here a continuous 

 supply of pressure water is pumped into the mains, with a velocity which 

 is in general so low that the kinetic energy is negligible. The potential 

 energy is also in general negligible, so that it is in virtue of the pressure 

 energy alone that the water is capable of doing work. If, however, the 

 pumps are stopped and the accumulators disconnected, the withdrawal of 

 a very few cubic feet of water from the mains will reduce the pressure to 

 that corresponding to the statical head at any point, and the capacity for 

 doing work to almost zero. 



Or consider an element of a stream tube of weight W, at a depth h 

 below the free surface, and at a height z above some datum. Its potential 

 energy is W z foot Ibs., while, in virtue of its position, its pressure energy 

 is W h, its pressure " p " being W h. 



Eemoved from its connection with the surrounding mass of fluid, which 

 guarantees the permanence of the pressure conditions for a finite period, 

 the potential energy is unaltered, but its available pressure energy is 

 now practically zero absolutely zero in the case of a perfectly incom- 

 pressible fluid. 



