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# atmospheric pressure

Atmospheric pressure is the pressure at any given point in the Earth's atmosphere. In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point. Low pressure areas have less atmospheric mass above their location, whereas high pressure areas have more atmospheric mass above their location. Similarly, as elevation increases there is less overlying atmospheric mass, so that pressure decreases with increasing elevation. A column of air 1 square inch in cross section, measured from sea level to the top of the atmosphere, would weigh approximately 14.7 lbf. A column of air would weigh about 100 kilonewtons (equivalent to a mass of 10.2 tonnes at the surface).

## Standard atmospheric pressure

The standard atmosphere (symbol: atm) is a unit of pressure and is defined as being equal to 101.325 kPa. The following non-standard units are equivalent: 760 mmHg (torr), 29.92 inHg, 14.696 PSI, 1013.25 millibars. One standard atmosphere is standard pressure used for pneumatic fluid power (ISO R554), and in the aerospace (ISO 2533) and petroleum (ISO 5024) industries.

In 1999, the International Union of Pure and Applied Chemistry (IUPAC) recommended that for the purposes of specifying the properties of substances, “the standard pressure” should be defined as precisely 100 kPa (≈750.01 torr) or 29.53 inHg rather than the 101.325 kPa value of “one standard atmosphere”. This value is used as the standard pressure for the compressor and the pneumatic tool industries (ISO 2787). (See also Standard temperature and pressure.) In the United States, compressed air flow is often measured in "standard cubic feet" per unit of time, where the "standard" means the equivalent quantity of moisture at standard temperature and pressure. However, this standard atmosphere is defined slightly differently: temperature = 20 °C (68 °F), air density = 1.225 kg/m³ (0.0765 lb/cu ft), altitude = sea level, and relative humidity = 20%. In the air conditioning industry, the standard is often temperature = 0 °C (32 °F) instead. For natural gas, the petroleum industry uses a standard temperature of 15.6 °C (60.08 °F), pressure 101.56 kPa (14.73 psi).

## Mean sea level pressure

Mean sea level pressure (MSLP or QFF) is the pressure at sea level or (when measured at a given elevation on land) the station pressure reduced to sea level assuming an isothermal layer at the station temperature.

This is the pressure normally given in weather reports on radio, television, and newspapers or on the Internet. When barometers in the home are set to match the local weather reports, they measure pressure reduced to sea level, not the actual local atmospheric pressure. See Altimeter (barometer vs. absolute).

The reduction to sea level means that the normal range of fluctuations in pressure is the same for everyone. The pressures which are considered high pressure or low pressure do not depend on geographical location. This makes isobars on a weather map meaningful and useful tools.

The altimeter setting in aviation, set either QNH or QFE, is another atmospheric pressure reduced to sea level, but the method of making this reduction differs slightly. See altimeter.

• QNH: The barometric altimeter setting which will cause the altimeter to read airfield elevation when on the airfield. In ISA temperature conditions the altimeter will read altitude above mean sea level in the vicinity of the airfield
• QFE: The barometric altimeter setting which will cause an altimeter to read zero when at the reference datum of a particular airfield (generally a runway threshold). In ISA temperature conditions the altimeter will read height above the datum in the vicinity of the airfield.

QFE and QNH are arbitrary Q codes rather than abbreviations, but the mnemonics "Nautical Height" (for QNH) and "Field Elevation" (for QFE) are often used by pilots to distinguish them.

Average sea-level pressure is 101.325 kPa (1013.25 mbar) or 29.921 inches of mercury (inHg) or 760 millimeters (mmHg). In aviation weather reports (METAR), QNH is transmitted around the world in millibars or hectopascals (1 millibar = 1 hectopascal), except in the United States and in Canada where it is reported in inches (or hundredths of inches) of mercury. (The United States and Canada also report sea level pressure SLP, which is reduced to sea level by a different method, in the remarks section, not an internationally transmitted part of the code, in hectopascals or millibars . However, in Canada's public weather reports, sea level pressure is instead reported in kilopascals , while Environment Canada's standard unit of pressure is the same ) In the weather code, three digits are all that is needed; decimal points and the one or two most significant digits are omitted: 1013.2 mbar or 101.32 kPa is transmitted as 132; 1000.0 mbar or 100.00 kPa is transmitted as 000; 998.7 mbar or 99.87 kPa is transmitted as 987; etc. The highest sea-level pressure on Earth occurs in Siberia, where the Siberian High often attains a sea-level pressure above 1087.0 mbar. The lowest measurable sea-level pressure is found at the centers of tropical cyclones.

## Altitude atmospheric pressure variation

Pressure varies smoothly from the earth's surface to the top of the mesosphere. Although the pressure changes with the weather, NASA has averaged the conditions for all parts of the earth year-round. The following is a list of air pressures (as a fraction of one atmosphere) with the corresponding average altitudes. The table gives a rough idea of air pressure at various altitudes.

fraction of 1 atm average altitude
(m) (ft)
1 0 0
1/2 5,486 18,000
1/3 8,376 27,480
1/10 16,132 52,926
1/100 30,901 101,381
1/1000 48,467 159,013
1/10000 69,464 227,899
1/100000 96,282 283,076

## Calculating variation with altitude

There are two different equations for computing the average pressure at various height regimes below 86 km (or 278,400 ft). Equation 1 is used when the value of standard temperature lapse rate is not equal to zero and equation 2 is used when standard temperature lapse rate equals zero.

Equation 1:

$\left\{P\right\}=P_b cdot left\left[frac\left\{T_b\right\}\left\{T_b + L_bcdot\left(h-h_b\right)\right\}right\right]^\left\{textstyle frac\left\{g_0 cdot M\right\}\left\{R^* cdot L_b\right\}\right\}$

Equation 2:

$\left\{P\right\}=P_b cdot exp left\left[frac\left\{-g_0 cdot M cdot \left(h-h_b\right)\right\}\left\{R^* cdot T_b\right\}right\right]$

where

$P$ = Static pressure (pascals)
$T$ = Standard temperature (kelvins)
$L$ = Standard temperature lapse rate (kelvins per m)
$h$ = Height above sea level (meters)
$R^*$ = Universal gas constant: 8.31432×10³ N·m / (kmol·K)
$g_0$ = Standard gravity (9.80665 m/s²)
$M$ = Molar mass of Earth's air (28.9644 g/mol)

Or converted to English units:

where

$P$ = Static pressure (inches of mercury)
$T$ = Standard temperature (kelvins)
$L$ = Standard temperature lapse rate (kelvins per ft)
$h$ = Height above sea level (feet)
$R^*$ = Universal gas constant (using feet and kelvins and gram moles: 8.9494596×104 kg·sq ft·s-2·K-1·kmol-1)
$g_0$ = Standard gravity (32.17405 ft/s²)
$M$ = Molar mass of Earth's air (28.9644 g/mol)

The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In these equations, g0, M and R* are each single-valued constants, while P, L, T, and h are multivalued constants in accordance with the table below. (Note that according to the convention in this equation, L0, the tropospheric lapse rate, is negative.) It should be noted that the values used for M, g0, and $R^*$ are in accordance with the U.S. Standard Atmosphere, 1976, and that the value for $R^*$ in particular does not agree with standard values for this constant. The reference value for Pb for b = 0 is the defined sea level value, P0 = 101325 pascals or 29.92126 inHg. Values of Pb of b = 1 through b = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when $h = h_\left\{b+1\right\}$.:

Subscript b Height Above Sea Level Static Pressure Standard Temperature
(K)
Temperature Lapse Rate
(m) (ft) (pascals) (inHg) (K/m) (K/ft)
0 0 0 101325 29.92126 288.15 -0.0065 -0.0019812
1 11,000 36,089 22632 6.683245 216.65 0.0 0.0
2 20,000 65,617 5474 1.616734 216.65 0.001 0.0003048
3 32,000 104,987 868 0.2563258 228.65 0.0028 0.00085344
4 47,000 154,199 110 0.0327506 270.65 0.0 0.0
5 51,000 167,323 66 0.01976704 270.65 -0.0028 -0.00085344
6 71,000 232,940 4 0.00116833 214.65 -0.002 -0.0006097

## Local atmospheric pressure variation

Atmospheric pressure varies widely on Earth, and these changes are important in studying weather and climate. See pressure system for the effects of air pressure variations on weather.

Atmospheric pressure shows a diurnal (twice-daily) cycle caused by global atmospheric tides. This effect is strongest in tropical zones, with amplitude of a few millibars, and almost zero in polar areas. These variations have two superimposed cycles, a circadian (24 h) cycle and semi-circadian (12 h) cycle.

## Atmospheric pressure based on height of water

Atmospheric pressure is often measured with a mercury barometer, and a height of approximately 760 mm (30 inches) of mercury is often used to teach, make visible, and illustrate (and measure) atmospheric pressure. However, since mercury is not a substance that humans commonly come in contact with, water often provides a more intuitive way to conceptualize the amount of pressure in one atmosphere.

One atmosphere (101.325 kPa or 14.7 lbf/sq in) is the amount of pressure that can lift water approximately 10.3 m (33.9 ft). Thus, a diver at a depth 10.3 meters under water in a fresh-water lake experiences a pressure of about 2 atmospheres (1 atm for the air and 1 atm for the water). This is also the maximum height to which a column of water can be drawn up by suction.

Low pressures such as natural gas lines are sometimes specified in inches of water, typically written as w.c. (water column). A typical gas using residential appliance is rated for a maximum of 14 w.c. which is approximately 0.5 PSI.

Non-professional barometers are generally aneroid barometers or strain gauge based. See Pressure measurement for a description of barometers.

## Atmospheric pressure's relation to water's boiling point

Although water is generally considered to boil at 100°C (212°F), water actually boils when the vapor pressure is equal to the atmospheric pressure around the water. Because of this, the boiling point of water is decreased in lower pressure and raised at higher pressure. This is why baking cookies at elevations above 3,500 feet above sea level requires special baking directions.

• Plenum
• NRLMSISE-00
• Barometric formula
• International Standard Atmosphere - a tabulation of typical variation of principal thermodynamic variables of the atmosphere (pressure, density, temperature etc.) with altitude, at mid latitudes.
• Barotrauma physical damage to body tissues caused by a difference in pressure between an air space inside or beside the body and the surrounding gas or liquid.

## References

* US Department of Defense Military Standard 810E
* Burt, Christopher C., (2004). Extreme Weather, A Guide & Record Book. W. W. Norton & Company ISBN 0-393-32658-6
* U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962.