I have tried all sorts of ways to introduce and to structure this chapter and have found it to be most difficult. The central problem is that steady swirling flow, that is, flow in circles, does not occur in nature but transient swirling flow seems to be everywhere. Normally when we try to analyse some device through which fluid flows we start with a flow pattern for steady flow, make some simplifying decisions and use the steady flow energy equation to find out what we can. Then we go back and take other effects into account. When you try to sort out the dynamics of swirling flow you can draw what looks like a flow pattern but is not an ordinary flow pattern in that every flow line is a circle and then you find that there is no obvious way to idealise the flow for analysis as there is for say, flow in pipes or flow over a weir because steady flow does not normally come back to flow through the same point. Yet swirling flow is used in separators and centrifugal casting and crops up in rotodynamic machines and causes no end of unwanted problems in unforeseen rotating flows. Mostly it is not a facility to make predictive calculations that is needed by the engineer but a familiarity with the behaviour of swirling fluids. This has found its form in the idea of a vortex and most people regard the word “vortex” as synonymous with swirling flow. However it seems to me that we need to reserve the word “vortex” for our models of swirling flow in the three forms of the forced vortex, the free vortex and the free spiral vortex.
I came to the conclusion that the most easily understood way to handle this is to recognise just two types of swirling flow, the forced vortex and the free vortex and to consider the mechanics of radial flow because it can co-exist with a free vortex to give the free spiral vortex. Then I can look at other types of swirling flow.