Endnote

I have spent many hours writing this chapter and the time has been necessary because of the sheer complexity of the behaviour of water in channels. The whole exercise has been based on much simplified models of the flow and these have proved to be very taxing in the mathematical manipulation needed to produce the most convenient forms of the ultimate expressions. However it seems to me that these simple models give the best value for effort in forming a mental model of the way the water behaves. They certainly make the observable behaviour of rivers and their fittings comprehensible.

 

This text has been confined to channels of rectangular cross section. There are other sections of which the large pipe running partly full and the trapezoidal section are the most common. The pipe is used for sewers and for drainage and the trapezoidal shape for surface channels because of the need to use diggers for their construction. The behaviour of water in these channels is the same as that for the rectangular channel and much of the quantifying is readily adaptable.

 

Of course I did not start from scratch and I am indebted to others for finding their way through the maze of different mathematical routes that might be possible. Sadly most of my effort went to filling gaps in the sequence that were covered by notes such as “by simplifying it can be shown that”. I found it to be enjoyable.