Is it true that the mass of air in normal atmospheric pressure over 1$m^2$ is 10326 $kg$?

Question

Is it true that the mass of air in normal atmospheric pressure over 1$m^2$ is 10326 $kg$? I calculated it from pressure formula

$p=\frac{F}{A}$.

Let $m=?, A=1 m^2 and p=101300 Pa$.

$p=\frac{F}{A} \Leftrightarrow ...\Leftrightarrow m= \frac{pA}{g}=\frac{101300 \cdot 1 }{9,81} = 10326 kg $. So why we don't feel that weight, because if $A=160 cm^2 = 160 \cdot 10^{-4} m^2$( the area of normal man s feet), then $m=\frac{pA}{g}=\frac{101300 \cdot 160 \cdot 10^{-4} }{9,81} =165 kg$.

Am I missing something? Why we don't feel that weight?

Answer 1

Your calculations are correct. The reason we don't feel it is because the 1 atmosphere of pressure will be applied to all surfaces of our body, including the soles of our feet. In fact the interior of our body is also pushing out against our skin with 1 atmosphere of pressure so there is no net force being applied in either direction at the skin's surface. The only way you could feel this pressure would be if part of your body was in contact with a vacuum while the rest of your body remained in air at 1 atmosphere of pressure. Imagine that you were standing on an opening to a vacuum chamber that was almost, but slightly less than the size of the soles of your feet. If there was a perfectly air tight fit between the vacuum opening and your feet, you would indeed feel that pressure as that much force on your feet just as you calculated. As a simpler experiment, just put your hand over the hose of a vacuum cleaner - that is only a very partial vacuum but the force you need to exert to remove your hand is due to the 1 atmosphere of pressure around us all pushing your hand onto the partial vacuum. In fact if you measured that force needed to pull your hand off of the vacuum cleaner hose, you could compute what the air pressure in the vacuum hose was.

Answer 2

You cannot simply recalculate the air pressure to mass (or weight) because the molecules in the air move in all possible directions, so they are not all acting simply down. But you can make the analogy that it is like having a 165 kg object on top of each of us.

And that is really true. There really is this pressure pressing on us from above, but we are just used to it. If you went somewhere with much lower pressure, you would feel the difference.