Gradually Varied Flow

In Chapter 4, we discussed uniform flowin which the flow depth remains constant with distance. Such flows occur only in long and prismatic channels(i.e., the channel cross section and bottom slope do not change with distance). In real-life projects, however, channel cross sections and bottom slopes are not constant with distance in natural channels and these are varied in constructed channels to suit the existing topographical conditions for economic reasons. In addition, hydraulic structures are provided for flow control. These changes in the channel geometry produce nonuniform flows while changing from one uniform-flow condition to another. As we discussed in Chapter 1, such flows are called gradually varied flows if the rate of variation of depth with respect to distance is small, and rapidly varied flows if the rate of variation is large. In other words, the flow depth changes gradually over a long distance in gradually varied flows and in a short distance in rapidly varied flows. Since the analysis of gradually varied flows is usually done for long channels, the friction losses due to boundary shear have to be included. These losses, however, may be neglected in the analysis of rapidly varied flows because the distances involved are short. In addition, the pressure distribution in gradually varied flow may be assumed hydrostatic because the streamlines are more or less straight and parallel. However, this is not the case in rapidly varied flows where significant acceleration normal to flow direction may be produced by sharp curvatures in the streamlines.

Steady, gradually varied flow is discussed in this chapter and the rapidly varied flow in Chapter 7. The gradually varied flow equations are first derived. The classification of various water surface profiles is then presented. This is followed by a presentation of procedures for qualitatively sketching the watersurface profiles and for determining the discharge from a reservoir. The watersurface profiles in compound channels are then discussed.