Flow in Channels

Fluid flow in open channels is characterised primarily by the exposure of a free surface to atmospheric pressure. For this reason the fluid concerned is always a liquid and nearly always water. Indeed rivers and canals, which together make up most instances of this type of flow, form a frequent and clearly visible part of the landscape. Problems connected with river and canal flow represent a high proportion of the work of the hydraulic engineer and the ease of access resulting from a free surface does not compensate for the increased complexity of such flows by comparison with flow in closed conduits. Water flowing in open channels is acted upon by all the forces that affect pipe flow with the addition of gravitational and surface tension forces that are the direct consequence of the free surface.

2.1.1 General. Gradually varied flow is non-uniform flow in which the change of depth in the channel occurs but gradually, in the direction of flow. As a result the streamlines in any restricted locality can be considered straight and parallel and the resulting pressure distribution will therefore be hydrostatic. This restriction on the flow conditions also enables the Bernoulli equation to be used to evaluate the fluid energy. It is known that the Bernoulli equation, as well as the hydrostatic pressure distribution, breaks down when the streamlines become significantly curved. The criterion of streamline curvature will be used to distinguish between gradually varied flow and rapidly varied flow although in practice the exact point of distinction is indeterminate.

At this point it should be made clear that open channel hydraulics is concerned with two principal types of channel, canals and rivers. The term canal is taken here to include all artificial channels regardless of their size and purpose and while the flow that takes place in these may be relatively complex the purpose for which they are designed and built is normally clear. On the other hand, a river* may fulfil a number of functions of use to man and it does not follow that those who are concerned at any one time with one particular function may fully appreciate all the others. Unfortunately, human interference with a natural river that is aimed at benefiting one of its functions will often affect many of the others, frequently adversely.

In this chapter, consideration is given to the relationship which exists between the flow in a channel and its boundaries. This relationship is only static, and therefore of no interest here, when the channel boundaries are non-erodible under all conditions of flow (concrete lined channels and canals) and when in addition, no water-borne sediment is introduced into the channel. In natural rivers and unlined canals the channel boundary is always erodible to a greater or lesser extent and sediment is carried into the channel both from the bed upstream and from the surrounding land. The flow in such a channel is always adjusting itself to the presence of this movable material whose behaviour in turn depends upon the action of the flowing water upon it. The whole will therefore form a single, highly complex, flow phenomenon: part fluid, part solid, in a channel of variable geometry.

6.1.1 Introduction. In considering unsteady flow in channels it is necessary to add time as a variable to the other combinations of hydraulic variables considered primarily in the first three chapters. By virtue of its free surface, unsteady channel flow is essentially non-uniform flow and it can therefore be conveniently considered in two categories, gradually varied and rapidly varied unsteady flow. Such a classification is made on the same basis as that used for steady non-uniform flow. The first category will have almost parallel streamlines, gradual changes in depth, vertical accelerations will play a minor part and channel friction forces a large one. The second category will be characterised by very pronounced curvature of the streamlines, rapid changes in depth and sometimes discontinuous water surface profiles, large vertical accelerations and channel friction forces of secondary importance.