Endnote

 

I think that there is something worrying in my problems with this chapter. During my teaching career I did not spot the inherent contradiction in deciding to treat the fluid as frictionless and to ignore counter rotation[1]. In some ways I feel deceived because it is normal for the simplifications that we make to facilitate analysis to be comprehensible whereas this decision leads us to an impossible position. It makes the treatment of swirling flow very difficult.

 

I used to lecture it quite happily in what I now recognise to be a simplified form. When I had time to stop and think about it I realised that swirling flow does not fit in with most other topics in engineering. We do not have important applications for swirling flow yet it occurs so frequently that it cannot be ignored. I think that I learnt a great deal more about this type of flow and I think that it has convinced me that wakes containing eddies are not just to be called an eddying wake and forgotten but seen to be an integral part of the flow pattern.

 

I have added some worked examples but they are trivial. The very nature of swirling flow makes the design of suitable examination questions very difficult. They either ignore the fundamental conflict of it being necessary to have fluid friction for the flow to exist at all and needing to pretend that the fluid is frictionless in order to analyse it or to produce exercises in mathematics.