22 BERNOULLI'S THEOREM APPLIED TO AN OPEN CHANNEL 



being accelerated, that is, in the condition in which pressure or elevation 

 head is being converted into velocity head. Under the reverse con- 

 dition, however, of converting velocity head into static head, there 

 seems to be an inherent tendency for impact to occur, causing excessive 

 turbulence and a corresponding decadence of kinetic energy into heat. 

 Thus, although theoretically velocity head and static head are mutually 

 interchangeable or convertible by a simple relation, in applying this 

 relation we have to remember that the change from velocity head to 

 static head can only be secured against obstacles, almost as though the 

 water were animated by a desire to avoid the change, and would avoid 

 it, if any way were open for it to do so. If the area of the stream 

 increases too rapidly in the downstream direction, the velocity will not 

 decrease uniformly. Part of the section will be filled with swiftly moving 

 water, and part with slowly moving water. Impact will inevitably 

 occur, and the energy lost in the resulting turbulence will prevent the 

 static head developed from being as large as that computed, assuming 

 only ordinary friction losses. 



The change from static head to velocity head, on the other hand, 

 occurs naturally and readily, with but little loss. 



With this in mind, the methods shown in Figs. 201, 202, and 203 

 may be compared. Experience shows that by Fig. 201, it is compara- 

 tively easy to secure the results desired. The water confined on all 

 sides cannot escape the transformation, and it is only necessary, for the 

 desired result, that the angle of divergence be sufficiently small. By 

 Fig. 202, the change is much more difficult. The water, being open at 

 the top, has a direction of possible motion and a source of disturbance 

 difficult to control. The place of particular danger is at N, the surface 

 of the water when flowing at the critical depth. At this particular place 

 the velocity head and elevation head are in a state of balance, the 

 rate of increase of the latter being exactly equal to the rate of decrease 

 of the former, so that the surface could take any other slope, even a 

 vertical one, without energy having to be supplied or taken away. 

 Being, then, in a state of unstable equilibrium, a very slight disturbance 

 could seriously modify its motion. 



Figure 203 shows the same condition of instability at the section of 

 critical flow, RS. Because of the convergence and divergence of the 

 flow, this method would probably be more difficult to adjust even than 

 that of Fig. 202. 



It is interesting to note that if the direction of flow is reversed, so that 

 the velocity is increasing instead of decreasing, all three methods would 

 work better. The first two methods, especially, could be made to follow 

 the mathematical curve quite closely. 



