the fact that the engine produces a rich warning at the end of the tank has everything to do with the flow resistance of the fuel in the fuel line. The flow resistance depends on the diameter of the pipe, the length of the pipe and the viscosity of the liquid.
Once the tank is empty, the feed pipe will start filling with air and the relative length of the pipe will decrease and therefore also the flow resistance. As a result, the fuel will gradually flow faster to the venturi, which gives a richening effect, until the tube is completely empty and the engine runs out of fuel , leans out and stops.
Interesting conjecture!
Another:
Given:
The engine "sees" the fuel head based on the point of regulation, i.e., the position of the uniflow tube outlet inside the tank.
When the uniflow tube outlet uncovers, the point of regulation is now the free surface of the fuel.
Important terms: fuel head, point of regulation, position of the uniflow tube, free surface of the fuel.
A thought process:
Assume the tank width exceeds the position of the needle valve.
Tank is draining, uniflow uncovers, fuel continuing to be drawn out, leaning out seen.
Until the fuel is all gone from the tank, remainder now in fuel line.
As that fuel in the line is consumed, the free surface of the fuel now moves back inboard towards the needle valve.
Resulting in a richening of the setting.
Hmmmmmm.