BRESSE'S BACKWATER CURVES 



65 



Channel bottom sloping upward, adverse slope. 

 A2, y greater than yc. 

 A3, y less than yc. 

 Boundary cases, such as that between the Ml and M2 curves, are 

 not included, for they represent either uniform flow, or conditions 

 impossible for continued flow. The twelve cases are shown in Fig. 602. 



^yr^^-^ _M^__l 



Horizontal 

 Asymptote 



Horizontal Asymptote 



'"'^"'''TSr---- 



Mild Slope 



CI 



»n=»e 



L 



Horizontal Asymptote 



Vz I 



Vc 



Horizontal 



Fig. 602. Backwater Curves. 

 Flow is from left to right in every case. 



For the flow to satisfy Bernoulli's theorem, the slope of the water 

 surface must equal the rate of change of velocity head with respect to 

 distance along the stream, plus the friction slope, so that 



d (V^\ 



