> As everyone learns in kindergarten, the speed at which water comes out of a spout in a tank depends on the height

What kindergarten did you go to? Maybe my public kindergarten education was seriously lacking.

> Ok, so, it’s the same as before, but the outlet of the spout is now significantly deeper / lower. So the speed of the water should be higher, right?

> Ok, but if the water is faster at the bottom of the long spout… We could view the top part of this system as an exact copy of the short-spout version. At the interface between the tank bottom and the pipe-spout, the velocity of the water should be the same as in the no-pipe version, right? But that means the water inside the pipe is accelerating inside the pipe:

No, it's not the exact same. In the top part of the long-spout system there's a lack of airpressure holding the water above it back compared to the short-spout, and quite a bit of cohesion in the water pulling the water above it down faster if the lack of air pressure isn't enough. The water in the whole system moves faster as a result.

You'd theoretically get the air (actually vacuum) bubble if you ran the experiment in a vacuum with a liquid that has no cohesion... liquids with no cohesion are otherwise known as gasses though and behave differently in other ways as well.

> in case someone wants to get nerdsniped https://github.com/kamilazdybal/fluid-toolbox

Really nice to see the process of thinking it through. This sort of thing gives a much better insight than just memorizing formulas.

Unfortunately nobody in the UK can see the images in the blog, 'cause imgur