The problem of divergent flow

We have the energy equation which has not been constructed for an idealised flow but is for one-dimensional flow and we plan to apply it to organised flow like the flow through a pipe or over a weir or through an orifice. Its success depends not on the validity of its application but on whether it serves our purpose as engineers. We shall see that it is very successful but we shall also run into limitations on its use. Unfortunately liquids cannot always flow in an orderly manner. In figures 4-11a ,b, c and d the elemental volume was shown as a converging tube and as a consequence the liquid accelerates as it flows through the elemental volume. The forces needed to produce this acceleration are caused by the pressures exerted on the liquid in the elemental volume and the inward acting side forces serve to ensure that the flow does converge. Clearly liquid can also flow through elemental volumes that diverge and then, if the flow is to diverge to fill the elemental volume, forces acting outwards must come into existence. For most of the mobile liquids this does not occur, the necessary forces do not come into existence and the liquid cannot find a condition of flowing in equilibrium in the same way as it does in convergent flow. The flow pattern breaks down into a mass of eddies and I need to offer some explanation and examples. I will do so in a later chapter.