Siphon and Level Simulator

Can I avoid sitting down for days and days with a pen and paper before I build something that doesn't work?

Unfortunatley No. The days of work are probably the only way. I have seen software that does modeling of water supplies used by larger concils etc but they are very expensive and used by so few people that they are not likely to ever become shareware. Once you start with a piece of paper and a pencil you might be suprised at how quickly it all makes sense

One could establish a mathematical model of the system that is based upon a program that produces timing 'ticks': at every tick, the levels and flowrates are recalculated across the system and the results displayed as required.

In the early 1980s, mathematical modelling was successful in predicting the tuning parameters needed in a three-term controller for a tight temperature control problem on a plant that was being built in rather a hurry. The controller was tuned on the mathematical model while the hardware was being assembled. The effects of altering the size of a tank, the temperature of the incoming water, the size of the heat exchanger, the stroke rate of the steam control valve and the response of the controller could all be assessed off-line. On start-up, the tuning parameters were simply transferred from the model to the real plant and hey presto! The plant worked correctly first time. The advantage in doing it this way was to save commissioning time.

Is BASIC still taught? It's probably all changed by now...

Happy days!

I'd have thought the equations governing the system could be derived and modelled somewhat as described above. Sadly as a mathematician I fail at the first fence.