258 HYDRAULICS AND ITS APPLICATIONS 



cap was screwed on to the idle end forming a " dead end," while in th 

 other the idle end of the tee was capped directly by a screw plug. 



(5) Losses at Sudden Changes in Section of the Pipe. These have bee 

 already considered in Art. 33. 



(6) Losses at the Exit from the Pipe. Where a pipe discharges belo^ 

 the surface, it is possible by using a diverging outlet, to convert a certai 

 proportion, up to about , of the kinetic energy of pipe flow, int 

 pressure energy. With this exception the whole of the kinetic energy i 

 dissipated in eddy production in the surrounding mass of water. 



With a given difference of surface level in the two reservoirs, the dept 

 of immersion of the pipe entrance or of its exit does not in the leas 

 affect the flow, since, although the difference of level between entranc 

 and exit is increased by lowering the exit or by reducing the depth c 

 immersion of the inlet, yet the pressure at which the water is discharge 

 is increased, and that at which it enters the pipe line is reduced, by 

 corresponding amount, so that the effective head producing flow i 

 unchanged. 



Where discharge takes place above the free surface, the pressure at th 

 exit is atmospheric, and the energy at this point exists solely in th 

 potential and kinetic form. If Ii e represents the height of the outle 

 above the free surface E, the equation of energy now becomes 



V 



or Z A [Z E -\- /ij = loss at entrance -f- losses in pipe + = , the who] 



* 9 

 of the kinetic energy being rejected in this case. 



Where a pipe is composed of a series of lengths having differer 



(v* \ 

 F 

 2 o ) 



V* 



where F ~ represents the loss in any length of pipe having the velocit 



^ ff 



of flow v. Since the velocities in the different sections of the pipe ar 

 inversely as the areas of these sections, the whole series of losses ca] 

 then be expressed in terms of a single velocity, and this having beei 

 determined the discharge may be calculated. 



\s an example of the application of this reasoning to the solution of i 

 specific case consider the following. 



EXAMPLE. 



A 6-inch main takes water directly out of the side of a reservoir at i 

 depth of 10 feet. At the end of the first mile, in the course of whicl 



