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Imagine I have an upside-down cone, which is filled with a gas - let's say it is air. At the bottom of this cone is an extremely small hole (a few microns in diameter). How do I go about calculating how much pressure is required for the gas to flow through this extremely small hole. In particular, I am interested in finding the threshold pressure, above which the air would flow through the gap and below which the air would not flow through the gap.

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  • $\begingroup$ What is upside down cone? Bottom narrow or wide? $\endgroup$ May 4, 2016 at 3:36
  • $\begingroup$ There is no non-zero pressure where the flow will be zero. You have a case of flow through an orifice. $\endgroup$ May 4, 2016 at 18:33

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A few micrometres is general gap between cotton shirt threads. Even as slight as 0.0000001Pa pressure difference should be enough for gas to pass, with atomic size being in nanometers.

If cone had water instead of air, surface tension would have prevented it. But because you fill cone with air, vanderwall forces here are very weak. So, surface tension is weakest or almost nil here.

The probability of gas particles to pass through holes although would reduce and more of particles would strike mesh rather than passing holes.

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  • $\begingroup$ Surface tension is only present when there are 2 phases involved. This is a single phase situation. $\endgroup$ May 4, 2016 at 4:19
  • $\begingroup$ @ChesterMiller Bhai sahab, Is cone made of air??? $\endgroup$ May 4, 2016 at 11:27
  • $\begingroup$ the fluid that is flowing is single phase, and the cone is rigid. So, in your best judgment, how does surface tension come into this problem. Please provide your aerodynamic differential equations that include surface tension. $\endgroup$ May 4, 2016 at 12:01
  • $\begingroup$ @ChesterMiller Surface tension tends to keep liquid drop spherical. There is an angle of contact between water and surface which causes causes bulging of liquid, disturbing surface tension. The phenomenon is applied to explain why water does not flow out of an inverted glass when covered at mouth with cloth. $\endgroup$ May 4, 2016 at 12:08
  • $\begingroup$ The only fluid in this problem is air. What have you got to say about that? Where is your interface with another fluid? $\endgroup$ May 4, 2016 at 12:29

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