2.2 - Atmospheric Pressure

Origin and Variation

Atmospheric pressure is caused by the weight of the layer of air acting on Earth’s surface and objects within the atmosphere.
It varies with weather and decreases at higher altitude, where the air is thinner.

A mercury barometer uses a glass tube about $1 m$ long, initially filled with mercury and inverted into a mercury-filled bowl.
Mercury falls to a stable height, leaving a vacuum above the column. Atmospheric pressure on the mercury in the bowl supports the column.
The vertical column height $h$ measures atmospheric pressure:

P_{atm} = h ρ g

For $h = 760 mm = 0.76 m$ , mercury density $ρ = 1.36 \times 1 0^{4} kg m^{- 3}$ and $g = 9.81 m s^{- 2}$ :

P_{atm} = 0.76 (1.36 \times 1 0^{4}) (9.81) = 101 396.16 Pa \approx 101396 Pa

This reading can also be stated as $760 mm Hg$ . Torricelli demonstrated support of the mercury column by atmospheric pressure in 1643.

Fortin barometer	Aneroid barometer
Uses changes in mercury-column height	Uses changes in the volume of a partial-vacuum metal box
Almost one metre high; large and difficult to carry	Small and portable
Takes longer to obtain a reading	Gives a direct reading quickly
Accuracy up to $\pm 0.1 mm Hg$	Accuracy up to $\pm 1 mm Hg$
Used at meteorological centres	Suitable for homes, ships and aeroplanes

In an Aneroid barometer, a mechanical system amplifies the small volume change of the metal box and moves a pointer.

Unit	Use or relationship
Pa	SI unit used in science; convert pressure to Pa before substitution into SI formulae
mm Hg	Medicine, meteorology, aviation and science; blood-pressure readings such as 120/80 use this unit
m H $_{2}$ O	Water pressure in seas, reservoirs and dams
millibar (mbar)	Meteorology; $1 mbar = 1 hPa$

Bakun Dam: Water pressure is $150 m H_{2} O$ .
Convert a liquid-column pressure into Pa using $P = h ρ g$ , with $h$ in metres. Convert Pa back into column height using $h = P / (ρ g)$ .
Blood-pressure example: With $ρ_{Hg} = 1.36 \times 1 0^{4} kg m^{- 3}$ and $g = 9.81 m s^{- 2}$ :

160 mm Hg \Rightarrow P = 0.16 (1.36 \times 1 0^{4}) (9.81) = 2.13 \times 1 0^{4} Pa

Seaside-wall example: For $P = 3.6 \times 1 0^{5} Pa$ and $ρ_{water} = 1.00 \times 1 0^{3} kg m^{- 3}$ :

h = \frac{3.6 \times 1 0 ^{5}}{( 1.00 \times 1 0 ^{3} ) ( 9.81 )} = 36.7 m

The pressure is therefore $36.7 m H_{2} O$ . Atmospheric pressure is about $1013 mbar$ ; at Mount Kinabalu’s summit it is about $60000 Pa$ .

At high altitude, oxygen absorption in the lungs decreases. Effects include faster breathing, increased metabolic rate, loss of appetite, dehydration and difficulty thinking clearly.
Mountain climbers: Prepare and train physically, carry equipment to monitor altitude, blood pressure and body temperature, ascend slowly to adapt to pressure changes, and drink water to prevent dehydration.
Aircraft: Pressurise the cabin to approximately sea-level pressure, circulate fresh air with adequate oxygen and maintain water intake during long flights.
Atmospheric pressure at Mount Kinabalu’s summit is about 60% of sea-level pressure; at commercial-aircraft cruising altitude it is about one quarter.
Outer space: Pressure is almost zero. Spacecraft need cabin pressurisation and an oxygen generator; astronauts outside the cabin need pressure suits to balance body pressure.

Water pressure increases with depth. Each additional $10 m$ adds approximately one atmosphere of water pressure. Actual pressure includes atmospheric pressure as well.
A diver at $30 m$ experiences about four times normal atmospheric pressure; a submarine at $240 m$ experiences about 25 times surface pressure.
Effects: Body tissues absorb excess nitrogen; nitrogen dissolves in blood; thinking becomes unclear. Rapid pressure reduction can form nitrogen bubbles in tissues or blood vessels.
Divers: Train for the high-pressure environment, wear a diving suit to reduce heat loss and ascend slowly to prevent nitrogen bubbles forming.
Submarines: Use a steel or titanium body with a circular cross section to withstand surrounding pressure. Maintain cabin pressure near sea-level pressure and supply oxygen using tanks or electrolytic generators.