CHANNEL IN WHICH FLOW IS CRITICAL AT ANY STAGE 49 



resenting the total head. This distance is hy = V^/2g. If the width of 

 water surface, T, can be expressed as a function of hv the shape of the 

 channel will be determined. Substituting A = Q/V in the above 

 expression 



Q 



hv = 



2TV 



or 



1 - 2W^ 1/2^^3/2 ' ^^ - 2^1/37^2/3 ' ^^"^^ 1/ - -V lgHr, 



Figure 406 shows the shape of this channel. The theoretical curves 

 come together an infinite distance downward, but since the area en- 

 closed is not infinite, it is possible to construct a rectangular bottom, 

 having the correct area and surface width. The stage must not be 

 allowed to descend into this bottom. There is only one such channel 



Fig. 406. 



For all depths of flow above the rectangular portion of this channel, the flow should be critical. 



for a given discharge. As far as is known to the writers, none has ever 

 been built. It would be interesting to build one, for except for the 

 influence of lateral components of velocity, the depth could change 

 over wide limits without energy being supplied or taken away. The 

 surface should be very unstable. 



Channel in which the hydraulic radius remains constant. This 

 channel has been an object of interest because of the theoretical pos- 

 sibility of constructing an earth canal that would be non-scouring and 

 non-silting over a wide range of stages. Representing the hydraulic 



