Where on earth did you get such a massive cardboard tube though?
I asked for tube in a local hardware stores selling floor carpet. The tube inside the carpet roll was rubbish for them, so I just got one for free and cut the lenght (1,2m) with a saw.
technically I think your setup would be considered negative pressure, since the chimney causes air to be drawn in through air pressure difference.
You're right about the sucking effect but the pressure is (and must be) the same inside the case and in the room. Intake vents must also be big enough to maintain the neutral pressure. If the pressure goes negative, the chimney starts to suck slower or even stop sucking, and the cooling wouldn't work.
Some additional physics of heat and pressure:
In houses with electric air contidioning and a fireplace with chimney a pressure difference causes a true problem sometimes - the smoke comes inwards. It happens when the pressure inside is smaller than outside. Same thing might happen even without electric air contitioning when weather is bad. At some point the pressure grows big enough (either by heat or enough of replacement air) and the chimney starts to work normally.
In computer cases the heat first causes positive pressure (expanded air) which tries to get out from the case wherever it can (pressure inside the case want's to achieve balance with pressure outside the case). Since the air is expanded, it's also lighter - so first direction is always upwards. If there are holes located higher and lower, the positive pressured air is exhausting from the higher one. After the balance in pressure is achieved, the flow of lighter air still goes on and tries to cause negative pressure. Replacement air starts to fill the gap (pressure ourside the case want's to achieve balance with pressure inside the case). Eventually all this physics cause a neutral pressure into the case (as long as the vents are big enough) and the heat remains the only thing that keeps the progress running. In all passive cooled systems this is the situation.
To maintain difference in pressure (in not sealed system) some force must be used all the time. Difference in pressure is againts the laws of nature.
In a chimney system positive pressure (caused by heat) is needed to start the flow - and the longer the pipe, the bigger the needed pressure. That's because there's always a natural pressure difference in the low and high ends of the pipe and that difference must be beaten. After the flow starts the system balances itself to neutral pressure. I suppose there is an optimal length for the chimney too, I don't know that. However please don't experience with this build with too long pipe
cause your case temperature might rise too high before the flow is able to start.
Has anyone ever tried a passive water cooling system? (without an active pump). It would be nice to know if natural convection also works with water in practice, especially if it works even better. I've also heard about a case totally filled with liquid, how's that?