It seems to me that mechanical engineers need some acquaintance with the behaviour of pipes when joined to form networks. The pipe system that most people come into contact with is the simple water-filled central heating system. I have drawn it diagrammatically in figure 9-1. The components are, the set of radiators, the heating coil for hot water, a boiler, a pump and the pipe-work. Radiators are of different sizes to give a heat output to suit the sizes of rooms. As a result the flow through each radiator should be proportional to the heat output that is required.
In the common arrangement two pipes, called the flow and return, of larger diameter than all the others are routed side by side through the structure of the building. Radiators and the coil are connected between the flow and return. The radiators and the coil are sited in the building often at the whim of the installer. The size of the pipes is chosen by some rule of thumb.
The routing of the pipe-work is determined either for minimum cost or to be least intrusive. As a result the lengths of pipe associated with any radiator is not selected to suit the hydraulic requirements of the system. Often the largest radiator is on the end of the longest pipe and vice versa. Valves are fitted at one end of each radiator with the idea of adjusting them to make the flow suit the intended output of each radiator.
We have seen just how non-linear such valves are and now, any adjustment of a valve in one pipe affects the flow through all the other pipes. There is very little chance that the system will operate as is intended and add to this the need for some sort of timed control and we are looking at a system that a mechanical engineer would find wanting in design. The business is best left to plumbers and tolerant house owners.
In engineering there are other much less complicated systems of pipes that are required to work as planned and it is prudent to have some acquaintance with both their behaviour and their analysis.
It turns out that only the very simple systems can be analysed at all except with expensive computers and software. We can look at two simple but useful systems to assess the difficulty.