Why pressure is a scalar instead of a vector? I know by definition that the pressure is the ratio of the force, which is perpendicular to the surface, to the area of that surface and it has no direction. But I am confused by the two questions concerning the 'direction' of pressure.


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*According to the definition, the force that corresponding to the atmosphere pressure is everywhere and to all directions in the air. This means that the   force due to atmosphere pressure in the  vertical direction is the same as that in the horizontal directions. This can not be understood intuitively because the gravity only acts vertically.

*For a compressional acoustic wave, such as that in the air or in the water, the direction of wave propagation is the same as that of particle vibrations. For a plane wave, the acoustic pressure at one point in space can be sensed from any directions since it is a scalar. Here comes the question: in the plane that is normal to the propagating direction, the particle velocity is zero wheras the acoustic pressure is not. But a nonzero pressure implies a nonzero force and a nonzero force will induce a movement. Consequently, the acoustic wave becomes transverse instead of compressional. Why?


Hope someone can help me. Thank you very much.
 A: Air pressure is not the direct effect of gravity; gravity only makes it so that pressure increases downwards. Pressure is the force exerted by molecules on neighboring molecules just because of the mutual repulsion when they get close. In a gas, where molecules are far apart, it's caused by collisions; in a liquid or solid the molecules are all bunched up, so pressure is just their resistance to being compressed.
This explains the fact that pressure acts in all directions. Gravity doesn't have anything to do with it per se; the force at a given point is the same in all directions because the molecules are constantly moving around and bumping into each other, and this moving and bumping is (at a given height) independent of direction. It does get stronger as you go down, because this bumping has to support the weight of the air above.
Regarding your second question, the answer depends on what velocity you're speaking of. Air molecules are constantly moving around randomly in all directions (remember that this is the source of pressure!). But on a relatively large scale (say, of the order of the wavelength of a sound wave), this random movement averages out, and we consider the air to be a rest. The back-and-forth movement in a wave happens on top of this random vibration, but it is not the back-and-forth itself that produces pressure.
