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The title really says it all: Why is this case? A "Feynman type" answer would be really appreciated as I'm more of a layman that a physicist.

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Quick answer, or demurral anyway. They don't. Feynman would have asked you to examine the evidence. – DWin Jan 7 '15 at 3:00
up vote 2 down vote accepted

The answer to this question is quite intuitive when you think about what pressure is: a force per unit area. In a high pressure zone, particles experience a high force, and in a low pressure zone, they experience a lower force. The high force "overpowers" the lower force, pushing the particles from the high pressure zone to the lower pressure zone.

You can also think about this from a statistical thermodynamics standpoint. Consider the following thought experiment: You have two containers, one with high pressure gas and another with lower pressure gas. The high pressure container contains a lot of particles per unit volume (that is, it's relatively "full"), and the lower pressure gas contains few particles per unit volume (it's relatively "empty"). When the two containers are put side to side and gas is allowed to flow, the "full," high pressure container will lose particles to the "empty," low pressure one, causing particles to move from high to low pressure again. Note that this effect is purely due to random movement of the particles. The equilibrium position, of equal particle densities everywhere, is simply the one that has the largest chance of happening (and an overwhelmingly large chance at that) in the long run.

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Thanks. Is the reason that the particles in high pressure zones receive more force, because there are more other particles nearby, each with a repulsive electrical force? is that correct? Is this the same reason we don't fall through a couch when we sit on it? – Baconbeastnz Apr 1 '14 at 21:57
Not quite. In chemistry and physics, we generally make a few simplifying assumptions about gases so we can treat them as "ideal gases." An ideal gas is a theoretical gas in which particles only interact through collisions, and not the electromagnetic force. Particles in a high pressure zone receive more force because there's a lot of other particles nearby, causing a lot of collisions. Each collision pushes the particle a little bit, so if there's a lot of particles, there will be a strong pushing force. – Shivam Sarodia Apr 2 '14 at 15:52
But what about particles exiting a Venturi tube; low pressure in tube; high pressure in the destination. Flow is NOT always along pressure gradient. You need to think about total energy. Feynman might have probably asked you to consider "action" but that's might not be a good perspective for thinking about local energy along streamlines. – DWin Jan 7 '15 at 2:57

You mention particles, so I'll provide a micro-scale analogy. In a gas or liquid, particles are always interchanging energy and momentum due to collisions with other particles. So we can treat them as if their velocity and direction is always random and changing.

Imagine a line in the middle of a field, with 10 people (say: $10^{22}$ particles in a typical amount of gas) on the left side, and 1000 people ($100 *10^{22}$ particles) on the right side. Every minute, every person rolls a dice and if it lands on one, moves to the other side of the field.

So let's see how the distribution changes, purely driven by randomness:

Seconds; # on left side, # on right side

0 10 1000

1 175 835

2 285 725

3 358 652

4 407 603

5 440 570

6 548 652

$\infty$ 505 505

Of course if you conduct this experiment, there will be some noise because of the small number of participants; with trillions and trillions of particles it will be a perfect equilibrium.

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I couldn't figure out a way to display them in a table, sorry :( – Kvothe Mar 30 '14 at 21:06
Your numbers don't add up. You start with 1010 at time 0, have 1100 at 1, 2, 3, 4 and 5, and end up with 1000. – LDC3 Mar 30 '14 at 21:17
Oops...Thank you. – Kvothe Mar 30 '14 at 21:20

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