CHAPTER VIII 

 ANALYSIS OF FLOW PROBLEMS 



It has been shown in the preceding chapters that the water surface, 

 for flow in a channel of non -varying cross section, may follow any one 

 of a number of different backwater curves. The water may also flow 

 uniformly at the normal depth, or it may go through a hydraulic jump. 

 Examples have been given of conditions under which each of the 

 numerous curves may form. The problem encountered in practice, 

 however, is different. Given a certain situation, such as a proposed 

 flume layout, the engineer is asked to predict the profile of the water 

 surface. The proposed layout may include a channel profile unlike 

 any of the familiar examples, so that an analysis of the particular 

 problem must be made. 



For the purposes of preliminary design, it will often be sufficient to 

 determine the general shape of the water-surface profile, with a few con- 

 trolling dimensions. This information will serve later as the starting 

 point of the detailed profile computations, if these are required for the 

 final design. It is not intended to formulate a set procedure by means 

 of which the water-surface curves may be determined for every possible 

 open-channel flow problem; instead, certain typical problems will be 

 worked out, which will serve to indicate the method of attack on prob- 

 lems that are more complicated in their detail. 



Changes of grade in straight channels of non-varying cross section. 

 Backwater curves form in uniform channels over changes of grade and 

 near the points of entrance and discharge. We consider first the dif- 

 ferent possible water-surface profiles which are caused by changes in 

 the bottom grade of the channel. There is assumed to be but a single 

 change of grade; the slope on each side is continued constant for an 

 infinite distance. This is equivalent to assuming that the next change 

 of grade, or other condition disturbing the normal flow, is sufficiently 

 far away to be of negligible effect. It also usually means that the 

 effects of the change of grade do not reach to the intake of the channel. 

 It will therefore be assumed, unless otherwise stated, that the dis- 

 charge is determined by some remote condition, and is known. 



The various cases for which sustained steady flow is possible under 

 the assumptions made are shown in Fig. 801. In each, the first step 



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