CHAPTER VI 

 BACKWATER CURVES — INTRODUCTORY 



To the layman, " backwater " means the water retarded above a dam 

 or backed up into a tributary by a flood in the main stream. He has 

 probably never thought of the existence of a transition between the level 

 pool and the unretarded stream above. Frequently, this transition 

 takes the shape of a long, smooth curve which is continuously concave 

 upward. It is this " backwater curve " that first commanded the 

 attention of hydraulicians. When it was found that other types of sur- 

 face profiles existed, an attempt was made to supply each with a suitable 

 name. Ultimately, however, twelve diff'erent types of surface curves 

 were found to be possible, and the selection of a distinctive and appropri- 

 ate name for each became well-nigh impossible. The term backwater 

 curve has come to be applied to all of them. The various types are 

 distinguished by criteria which will be explained in this chapter. 



Longitudinal water-surface curves, in general, include not only back- 

 water curves, but also profiles through the hydraulic jump, over weirs, 

 around bends, and past changes in the cross section of the stream. In 

 phenomena due to sudden changes in direction or cross section, vertical 

 or lateral components of velocity play such a large part that they cannot 

 be ignored. On the other hand, the profile of a backwater curve is 

 always comparatively flat, changes in section are gradual, and vertical 

 and lateral components of velocity may be neglected without intro- 

 ducing appreciable error. 



We shall consider only steady flow, that is, the condition in which the 

 flow at each cross section remains constant with respect to time. For 

 the existence of a backwater curve the flow is non-uniform. The study 

 of backwater curves is complicated by the large number of independent 

 variables. It seems desirable, therefore, to study first the simplest 

 cases having practical utility. 



Backwater curves in a frictionless rectangular channel. It was 

 shown in Chapter II that if a frictionless channel has a level bottom, in 

 general, there can be no variation in depth of flow or in velocity. The 

 backwater curve reduces to a simple, horizontal, straight line. If the 

 bottom slopes, surface curves are possible, in accordance with Bernoulli's 



60 



