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Air will flow from areas of high pressure to areas of low pressure.

Pressure = force/area.

So in this context, air pressure is the force the particles in that area exert on the space around them (let's imagine they're in a box). As air particles whizz around, they will collide with the edges of the box, so bouncing off and changing direction. This direction change involves a lot of acceleration (though speed may be the same, velocity (which is speed in a specific DIRECTION) will be very different.

Physics tells us F=MA. Therefore, this acceleration will equate to a force on the outside world. This force will therefore be proportional to the number of particles in the area (more particles = more area).

So, if an area of high pressure has lots of particles, there will be a spreading out of these particles to areas of low particles (diffusion, and energy's natural tendency to spread out). Alternatively, think of it as particles in the high pressure area pushing against the particles from the low area, and they're pushing force being greater, so they win!

There you have a very long winded answer for why air moves from high pressure to low pressure!

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