Atmospheric Pressure

The Earth's atmosphere exerts pressure on every surface due to the weight of air above. Standard atmospheric pressure at sea level is approximately $1.013 \times 10^5$ Pa = 760 mm of Hg = 1 atm.

Concept

Torricelli (1643) measured atmospheric pressure using a tube filled with mercury inverted into a mercury reservoir. The height $h$ of the mercury column corresponds to atmospheric pressure: $P_{\text{atm}} = \rho_{\text{Hg}}\,g\,h.$

With $\rho_{\text{Hg}} = 13600$ kg/m $^3$ , $g=9.8$ m/s $^2$ , $h=0.76$ m: $P_{\text{atm}} \approx 1.013 \times 10^5$ Pa.

Manometer (open-tube U-shaped): measures gauge pressure of a gas by the height difference of liquid in the two arms: $P_{\text{gas}} = P_{\text{atm}} + \rho g h.$

Derivation

For the mercury barometer:

The closed top of the tube above the mercury column is essentially vacuum (vapour pressure negligible).
At the level of mercury in the reservoir, pressure inside the tube = pressure outside = $P_{\text{atm}}$ .
From hydrostatics: $P_{\text{vacuum}} + \rho_{\text{Hg}} g h = P_{\text{atm}}$ , giving $P_{\text{atm}} = \rho_{\text{Hg}} g h$ .

The height is independent of the tube cross-section or orientation (as long as the tube is long enough).

Worked Example

A patient's blood pressure is reported as 120/80 mm Hg. Convert systolic 120 mm Hg to Pa.

$P = \rho g h = 13600 \times 9.8 \times 0.120 = 1.6 \times 10^{4}\,\text{Pa}.$

This is the gauge pressure (above atmospheric).

Common Confusions

A barometer reading $760$ mm Hg means atmospheric pressure pushes mercury up by that height — there is no air pushing it down inside the tube.
The reading does not depend on tube area; only height matters.
Pressure decreases with altitude — by about 1 mm Hg per 11 m near sea level.

Key Takeaways

$P_{\text{atm}} \approx 1.013 \times 10^5$ Pa = 760 mm Hg = 1 atm.
Mercury barometer: $h = P_{\text{atm}}/(\rho g)$ .
Manometer measures gauge pressure via height difference.