How can air pressure be equal in all directions? Lay on the ground in a bright sunny day of spring and look the sky. Feel the air pressure on you.
Now lay on your stomach and your back exposed to sky.
You won't feel any change in air pressure. You will breathe normally. Even though air above you ( below you actually ) is so less that it cannot exert the same force/pressure on you.
I know that at a horizontal plane, pressure in fluids is same in all directions but why is it that way?
Its like someone is applying a force or exerting a pressure on you from above but you feel the same force/pressure from all directions, even from sideways. (Maybe the same pressure from downwards can be explained by Newton's third law but even from sideways, the same thing?)
I think fluid particles' mobility is the cause of it.
 A: Actually, the weight of the air above you contributes to the pressure that you feel. Because of this, air pressure drops as you go to higher altitude. This change is not so significant on the scale of you turning your head from pointing down to pointing up, so no real change is noticeable.
Why does pressure only depend on altitude and not change when you walk around at the same altitude (in a simplified model)? Since the earth is mostly spherical, the atmosphere is mostly spherical, so at any point on the earth's surface there is the same total weight of air from the atmosphere on top of you.
I think some of your questions are easier to understand when we remember that pressure is force divided by area. To hold up the weight of the atmosphere, the particles at the surface have to push back. The more they push back, the faster they must be moving on average. Now, the direction of their movement can be in three dimensions, so they not only push up by also push horizontally. The average force contributed by these particles is the same in all directions, which is why the pressure is the same in all directions.
