# Closed tube Mercury Barometer cancels pressure of air above the tube?

Barometers are supposed to measure the air pressure, however I do not understand why there is 0 pressure on top of the closed tube. According to my understanding, if the pressure acting on the mercury on the open sides is Patm, the sum of the pressure at the same level but on the bottom of the closed tube from bottom up should be:

ρ_Hg*g*h_Hg + P_vacuum + P_AirAboveTube

= ρ_Hg*g*h_Hg + 0 + (Patm - ρ_air*g*h_tube)

Equalling them will result in:

Patm = ρ_Hg*g*h_Hg + Patm - ρ_air*g*h_tube

ρ_Hg*g*h_Hg = ρ_air*g*h_tube

Which means the pressure by the mercury that rose in the tube should equal the pressure of air from the top of the mercury on the sides to the top of the barometer tube, which is not a lot, hence the mercury shouldn't rise... which is not what's observed in real life

My question is, why is there no "P_AirAboveTube" acting on the mercury in the tube, how does this vacuum on top of the tube somehow eliminates it? Is it just because there is no medium for the P_AirAboveTube to act on, or is it something else?

I do not understand why there is 0 pressure on top of the closed tube.

There is air pressure on top of the closed tube. If you're talking about a barometer near sea level, then there is approximately one atmosphere of pressure on top of the tube. But pressure on the tube does not affect the reading. It's the pressure inside the rigid, closed tube that matters.

The pressure on the top of the mercury column, inside the tube, practically is zero.*

why is there no "P_AirAboveTube" acting on the mercury in the tube?

There is no air inside the tube because of how the barometer is made. To make a mercury barometer, you hold the tube with the open end facing up, and you fill it with mercury all the way to the rim. Then, you cover the opening, being careful not to trap any air, you invert the tube (covered, open end facing down), being careful not to let any air in or mercury out, and you submerge the open end in a pool of mercury. Finally, you uncover the submerged, open end.

Assuming that the tube is sufficiently long (more than 760mm), then the level of mercury will drop when you uncover the open end, and the space above the top of the mercury column will be vacuum.

The reason the column drops is because of the weight of the mercury in the tube. The reason it doesn't drop further is because the pressure of the mercury in the pool, which is equal to atmospheric pressure right at the surface, supports the weight of what remains in the tube.

The space above the mercury will be filled with mercury vapor. But the vapor pressure of mercury at room temperature is negligible.