This is a bench-scale, two-dimensional approximation of a Heron's fountain. Water falling from the Basin through the active intake enters the lower sealed chamber and compresses the air shared through P2. That pressure drives water from the upper chamber through the active nozzle and back into the Basin.
Invert pauses physics for one real second while the chambers exchange elevations, then reverses the roles of P1 and P3. Auto Invert can use jet speed, flow rate, chamber fill, cycle time, or the settled state as its trigger.
The model conserves water volume and approximates pipe flow and shared-air compression. It intentionally simplifies turbulence, temperature changes, pipe transit time, and detailed flexible-tube mechanics.