64 BACKWATER CURVES — INTRODUCTORY 



be rectangular, and infinitely wide, 



-21 



•5/ = 7^27 = :;S-3 [604] 



The subscript / distinguishes the friction slope from the water surface 

 slope Sw and the bottom slope 5o. To use Chezy's formula in this way 

 is to assume that the rate of loss of energy through friction, at a given 

 section, is the same in non-uniform flow as it would be for uniform flow 

 at the depth of flow existing at that section. This is not strictly true 

 because expanding flow tends to be more turbulent, and contracting 

 flow less turbulent, than uniform flow. The error from this source is 

 small when the rate of contraction or expansion is small, which is the 

 case with backwater curves in uniform channels. 



For a given quantity of flow, channel shape, slope, and roughness, a 

 certain depth of flow will be just right to maintain uniform flow. As 

 noted before, the surface slope, the friction slope, and the bottom slope 

 are equal for uniform flow, so that for an infinitely wide rectangular 

 channel this depth, termed the normal (or neutral) depth, is determined 

 by Chezy's formula to be 



The normal depth is of great importance. Together with the critical 

 depth and the bottom slope, it forms the basis for the classification of 

 all possible backwater curves, according to the following outline: 



Channel bottom sloping downward. 

 jn greater than yc, mild slope. 



Ml , y greater than yn- 



M2, y less than yn but greater than yg. 



M3, y less than yc. 

 yn less than yc, steep slope. 



51, y greater than yc. 



52, y less than yc but greater than y„. 



53, y less than yn- 



yn equal to yc, critical slope. 

 CI, y greater than yc- 

 C3, y less than yc. 

 Channel bottom horizontal. 

 H2, y greater than yc. 

 H3, y less than yc. 



