Can an Adequately Long Tube Float?

Question

I was just pondering in my head one day (I don't recall what I was pondering), but I came across the thought: If an adequately long (and light) tube is placed in the atmosphere, can the difference in air pressure from one end to the other cause the tube to float?

The formula for air pressure at a given altitude is: Pressure $p= p_0e^{-(h/H)}$, where $p_0$ is the pressure at sea level (about 101,325 Pascals), $h$ is the height, and $H$ is the scale factor (which is about 8 km for average outdoor temperatures).

If we ignore the math and actual design, is this idea plausible?

If it is plausible, what would the dimensions of the tube have to be if the end area is 0.1 square meters?

(Sorry about running out of time to show any of my work before asking this question)

Answer 1

The tube would need to be evacuated and sealed off to float in air. However, it would be crushed by atmospheric pressure or it will be be too heavy to float. Some modified designs (say, a spherical sandwich structure) can be viable.

Answer 2

The air inside the tube would change pressure with altitude just like the air outside. After all, outside air pressure is nothing but the weight of air above.

However, you can reduce the density of the air by raising its temperature. If you have a volume of air that has the same pressure as the air outside, but lower density, it will experience buoyancy. That is how hot-air balloons work.