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If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside.

If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) pressure inside be? Can it be -20 psi / -1.5 bar / -150 kPa?

Absolute pressure can't be negative, right?

Brandon Enright
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Rudie
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    Related:http://physics.stackexchange.com/q/65637/, http://physics.stackexchange.com/q/57556/ – Kyle Kanos Dec 16 '13 at 20:34
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    @KyleKanos The video in a comment in one of those questions is about negative pressure in trees: -15 atm and less. Very cool! Thanks! – Rudie Dec 16 '13 at 20:54

2 Answers2

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You can absolutely have negative absolute pressure in solids or liquids. Think of an elastic solid being forced to expand due to adhesion to the walls of some chamber. That has negative pressure even if the comparison is a total vacuum. Depending on the bulk modulus of the material being stretched and the strength of the interaction with the walls of the chamber holding the material, you may be able to get to several negative atmospheres of pressure.

Dark energy also creates negative pressure in otherwise empty space.

See this veritasium video for more about negative pressure in trees.

Dan
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  • I don't understand the elastic solid... I saw the tree video. Trees apparently have airless chambers to suck up water? I didn't get that either. Maybe the 'less than nothing' is too vague for me. Please tell me more. – Rudie Dec 16 '13 at 23:24
  • @Rudie: The idea is that the pressure in two regions can be compared by putting a movable piston in between them. If there is no net force on the piston, the pressure difference is zero. Otherwise, the pressure will push the piston to the region with lower pressure. If I attach a spring to one of the sides of the chamber, and expose the other side to a vacuum, the piston will come to some equilibrium position. I can then force the piston even further towards the vacuum side. Since the force on the piston is towards the spring, the spring side must have lower pressure than the vacuum. – Dan Dec 16 '13 at 23:43
  • @Rudie: Think of it this way: Pressure is force per unit area. Force can be negative (pulling on the surface instead of pushing on it), so pressure can be negative too. – Dan Dec 16 '13 at 23:46
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    It might be worth noting in the text that this is an idea that (1) rarely appears in everyday life and (2) took a while to be accepted historically. – dmckee --- ex-moderator kitten Dec 16 '13 at 23:55
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You're right, absolute pressure can't be negative. Of course, you can easily have a $20\: \mathrm{PSI}$ pressure differential (although not without pressure above $1\: \mathrm{ATM}$ since that's $14.22\: \mathrm{PSI}$ at sea level). Check out Wikipedia on the zero-reference:

  • Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure.
  • Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted. To distinguish a negative pressure, the value may be appended with the word "vacuum" or the gauge may be labeled a "vacuum gauge."
  • Differential pressure is the difference in pressure between two points.
Brandon Enright
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  • So the pressure gauge measures the difference? Not actual pressure? How? Does it measure inside and outside separately? – Rudie Dec 16 '13 at 20:37
  • @Rudie Indeed, gauges measure a pressure difference. Usually the gauge measures against the outside air pressure (usually $1: \mathrm{ATM}$) but there is no reason why a gauge couldn't read the difference between two different chambers that are themselves different than the ambient pressure. – Brandon Enright Dec 16 '13 at 20:41
  • Wait, I seem to recall that (for example) trees have negative pressure gradients to transport water from the roots to the tips of the tree. The thermodynamics / risks of embolism inside of xylem tubes is a real concern. http://en.wikipedia.org/wiki/Xylem#Cohesion-tension_theory –  Dec 16 '13 at 21:06
  • @sakanojo that's negative pressure compared to the ambient air pressure around the tree. Negative pressure (a pressure differential) is possible, just not negative absolute pressure. – Brandon Enright Dec 16 '13 at 21:09
  • @Brandon Enright: You can absolutely have negative pressure in solids or liquids. Think of an elastic solid being forced to expand to to adhesion to the walls of some chamber. That has negative pressure even if the comparison is a total vacuum. – Dan Dec 16 '13 at 22:12
  • @Dan so you'd consider something like rope tension to be negative pressure? That's a pretty non-traditional view but it seems pretty reasonable. – Brandon Enright Dec 16 '13 at 22:18
  • @Brandon Enright: That's a one-dimensional view of things, but it works out I suppose. I was thinking of a liquid that sticks to the sides of its container. If the adhesion of the liquid to itself and to the container was large enough, you could expand the container arbitrarily. If you had a piston with this liquid in one chamber and vacuum on the other, it would reach some equilibrium position, and could also be stretched beyond this equilibrium. – Dan Dec 16 '13 at 22:23
  • @BrandonEnright In solid mechanics, negative pressure representing tension is okay when using the unloaded pressure as 0. But the definition of absolute vs. gauge is a bit unclear in solids where it's really just about where you define the zero point. – tpg2114 Dec 16 '13 at 22:29
  • @tpg2114: I would argue that the zero point should be defined as a hyrostatic equilibrium with the vacuum. – Dan Dec 16 '13 at 22:37
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    @Dan That's also a valid argument. However, it's really chosen differently by different authors, and one choice is that the unloaded configuration has zero pressure, which is consistent with the notion that pressure is the trace of the stress tensor. So tension (negative stress) generates a negative pressure. – tpg2114 Dec 16 '13 at 23:09
  • @tpg2114: That works too. – Dan Dec 16 '13 at 23:44