The study of open channels

Water flows in a channel when the channel connects a source of water at one level to a discharge point at some lower level and it is the gravitational field that sustains the flow. The flow is resisted by “friction” forces that are of the same character as those in pipes. The most common channels are natural water-courses, that is rivers and brooks, and man-made ducts such as canals and drainage channels. These channels can vary from smooth-surfaced, straight, unobstructed channels to rough, winding channels full of weed. Man-made channels usually have geometrical shapes, typically trapezoidal, rectangular, circular or semi-circular and perhaps parabolic. The problem of quantifying the friction loss in such channels is even more formidable than that for pipes.

 

The downward slope in normal channels is very small. I cannot detect the slope when I walk along the banks of the River Medway in Kent in England yet many rivers have much smaller slopes. It would be difficult to detect the slope of the surface and even more difficult to decide whether the slope of the surface was the same as that of the river-bed. Yet civil engineers need to understand the mechanics of such rivers and mechanical engineers are no worse off if, when they see water flowing in a river, they can answer the question “ why does it do that?”

 

Channels are generally long with fittings occurring at intervals for various reasons. On rivers it is common to have fixed weirs that are associated with locks, to make the river navigable. Rivers have seasonal variations of flow and the weirs usually have adjustable gates that normally cope with these changes but may well be overwhelmed in time of flood. There are other man-made channels that are often straight and made with a uniform section in ways that depend on the nature of the ground through which the channel has been cut. Some have sections with sloping sides to suit the use of digging machines, others are lined with very smooth concrete with vertical sides. Treatment works use channels in various ways. These man-made channels also employ fittings for various purposes.

 

Just walking alongside such channels leads the engineer to doubt whether any analysis is possible. Certainly the flow is going on in the open and subject to all sorts of natural activity like weed growth, algae growth, organic and non-organic debris that may not be visible and the effects of the wind.[1]  An engineer might ponder how the speed of the flowing water might be measured and conclude that it cannot be easy. I do not think that he would immediately think of a double float, a hunter watch and a man on horseback. I am pointing out that the study of channel flow is never going to be as amenable to analysis as say the use of the aerofoil in the wings of an airliner. It is a difficult topic to study and it will always be subject to random and unpredictable effects. The best that we can do is to try to understand the behaviour of water in channels and exercise our engineering skill to make the best shot we can at design. My impression is that over the years this study has become very successful even through the use of empirical methods.

 

The study of channels can be in two sections, the study of the long runs of channel and the study of the fittings but both depend on the same physics and so that is where I must start and it is the Bernoulli equation, adapted to channels, momentum and continuity on which it all depends.