Suppose we have a cylindrical glass at atmospheric pressure. The glass is put in a horizontal position such that the bottom of it (the closed end) is at the right side and the open side is on the left.

Is it possible to create vacuum in the glass just by accelerating it to the right fast enough? And if it is, how can one calculate an approximate value for it?

  • $\begingroup$ I highly recommend XKCD's what-if.xkcd.com/6 . While XKCD is not exactly what I would call it a "academically credible source," it is well researched, and far more funny than any other source out there. $\endgroup$ – Cort Ammon Feb 22 '15 at 14:10

You can certainly create a pressure gradient. Depending on the acceleration, that gradient could be as large as you like and could lead to a very low pressure at the front, which might approach a vacuum. The equation is very simple:

$$ \Delta P = - \rho g \Delta h $$

So for a $1m$ tube, filled with ambient air ($\rho = 1.2754\ kg/m^3$) and a $1g$ acceleration, you'd get $\Delta P = 12.5 Pa$.

Twelve Pascals isn't very much (sea-level air pressure is about 100,000 Pa).

To get a rough vaccum, (so $\Delta P = 10^5 Pa$), with a $10m$ tube, you'd need $a = 10^5 / 1.2754 \times 10 = 7840\ ms^{-2}$ or about $800g$.

Once you've evacuated the tube, it will not refill as long as it maintains a velocity greater than the ambient velocity of air particles (about $500\ ms^{-1}$). However, that's the average velocity. The actual velocits of an individual particle is Boltzmann-distributed so a few might be going fast enough to leap aboard. Then there's turbulence and the Venturi Effect and other aerodynamic complications.

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