With simplifying assumptions
If we assumed that :
- Earth has the same mass density everywhere for a given distance away from its center (uniform radial mass density)
- There are no external gravitational fields (Like the pull of the moon and the sun, which vary depending on what side of Earth is closest to those bodies)
- There are no internal friction forces from the level's internal forces or within the fluids themselves.
Then the bubble would have no preference for any position in the level and it would stay wherever it happened to be first when the construction of this hypothetical level was completed.
Dropping Assumptions
But Let's drop those assumptions one by one and see what happens:
1. Earth is not a perfect, smooth sphere
Without having to do any analysis of Earth's crust and mantle, we could tell that there are places on earth with more material in them. We don't even have to know anything about density, but it's straightforward to observe, even if everything on earth (not including the atmosphere here) was made up of the same exact material, that there are places with just more stuff.
Standing on top of Mount Everest (~29,000ft above sea level), you have more stuff between you and Earth's geometric center than you do if if you were standing on the shores of the Dead Sea (~400ft below sea level).
But furthermore, stuff do have different densities, and so it becomes safe to assume that we're not gonna have uniform mass density around Earth, and therefore the gravitational field is not gonna be uniform either.
One important consequence of this is that the alcohol in our level will want to be as close as possible to the most amount of material, pushing our bubble halfway across the world from that point.
A good candidate for this would be somewhere in Indonesia or Ecuador, but I can't say much more without a defined altitude.
2. There are other sources of gravity
Earth and everything on it, including our level, are subject to external gravitational fields.
If you've spent some time around large enough bodies of water, like an ocean, you'll have noticed that the water level changes throughout the day. That in short happens because as the moon orbits our planet, its distance to different parts of Earth's surface changes, and so does its gravitational pull.
This can impact our bubble's position in two, directly related ways:
- As the moon gets closer to one part of our level, it will both attract more water beneath it, which will increase the gravitational attraction force the alcohol experiences towards the Earth.
- But it will also attract the alcohol inside of our level towards the moon, and away from the Earth.
The net result of those two effects will again depend on our level's altitude, and how close it is to bodies of water.
Keep in mind that if we didn't drop the assumption that Earth had uniform mass density, then our bubble would move in perfect sync with moon, except it would be on the opposite site of the planet, 180 degrees ahead.
The sun is large enough and far away enough that variation in the gravitational force is negligible if we're well within Earth's atmosphere
3. Friction
Finally, moving around in a tube requires some energy to overcome the friction with its internal walls.
On top of that, the fluids (alcohol and air) themselves both have internal friction forces that oppose relative motion of one part of the fluid with respect to another. This is what we call a viscosity.
If our bubble's "preferred position" (lowest potential energy position) is not "much better" (significantly lower potential, on the order of magnitude of the friction force) than our current point, then the difference is not strong enough to persuade our bubble to move.
Consequently, our bubble might settle in one place forever, or periodically travel from one point to another, settling in position until those frictional forces are overcome by gravitational variation.
