Atmospheric pressure

"Air pressure" redirects here. For the pressure of air in other systems, see pressure.

Atmospheric pressure is defined as the force per unit area exerted against a surface by the weight of air above that surface 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 one square inch in cross-section, measured from sea level to the top of the atmosphere, would weigh approximately 14.7 lbf (65 N). The weight of a 1 m² (11 sq ft) column of air would be about 101 kN (10.3 t_f) .

Altitude atmospheric pressure variation

This plastic bottle, sealed at approximately 2,000 m (6,600 ft) altitude, was crushed by the increase in atmospheric pressure when brought to sea level.

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/e	7,915	25,970
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	86,282	283,076

Calculating variation with altitude

See also: Barometric formula

There are two different equations for computing the average pressure at various height regimes below 86 km (53 mi; 282,000 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:

${P}=P_{b}\cdot \left[{\frac {T_{b}}{T_{b}+L_{b}\cdot (h-h_{b})}}\right]^{\textstyle {\frac {g_{0}\cdot M}{R^{*}\cdot L_{b}}}}$

Equation 2:

${P}=P_{b}\cdot \exp \left[{\frac {-g_{0}\cdot M\cdot (h-h_{b})}{R^{*}\cdot T_{b}}}\right]$

where

$P_{b}$ = Static pressure (pascals, Pa)

$T_{b}$ = Standard temperature (kelvin, K)

$L_{b}$ = Standard temperature lapse rate (kelvin per meter, K/m)

$h$ = Height above sea level (meters, m)

$h_{b}$ = Height at bottom of layer b (meters; e.g., $h_{1}$ = 11,000 m)

$R^{*}$ = Universal gas constant: 8.31432 Nm/(K·mol)

$g_{0}$ = Standard gravity (9.80665 m/s²)

$M$ = Molar mass of Earth's air (0.0289644 kg/mol)

Or converted to Imperial units:

where

$P_{b}$ = Static pressure (inches of mercury, inHg)

$T_{b}$ = Standard temperature ([[kelvin]s, K)

$L_{b}$ = Standard temperature lapse rate (kelvin per foot, K/ft)

$h$ = Height above sea level (feet, ft)

$h_{b}$ = Height at bottom of layer b (feet; e.g., $h_{1}$ = 36,089 ft)

$R^{*}$ = Universal gas constant; using feet, kelvin, and (SI) moles: 8.9494596×10⁴ gft²/(mol·Ks²)

$g_{0}$ = Standard gravity (32.17405 ft/s²)

$M$ = Molar mass of Earth's air (0.0289644 kg/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 P_b for b = 0 is the defined sea level value, P₀ = 101325 pascals or 29.92126 inHg. Values of P_b 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 $h=h_{b+1}$.:

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	-0.00649	-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	0.0327505	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

Hurricane Wilma on 19 October 2005–88.2 kPa (12.79 psi) in eye

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 millimetres (30 in) of mercury is often used to 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 visualize the pressure of one atmosphere.

One atmosphere (101.325 kPa or 14.7 psi) is the amount of pressure that can lift water approximately 10.3 m (34 ft). Thus, a diver 10.3 m underwater experiences a pressure of about 2 atmospheres (1 atm of air plus 1 atm of 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) or W.G. (inches water gauge). A typical gas using residential appliance is rated for a maximum of 14 w.c. which is approximately 0.034 atmosphere.

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

Boiling point of water

Boiling water

Water boils at approximately 100 °C (212 °F) at atmospheric pressure. The boiling point is the temperature at which 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 at elevations more than 3,500 ft (1,100 m) above sea level requires adjustments to recipes. A rough approximation of elevation can be obtained by measuring the temperature at which water boils; in the mid-19th century, this method was used by explorers.

See also

• Atmosphere (unit)
• 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.
• Subtropical high belts

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.

External links

• How Atmospheric Pressure Affects Objects (Audio slideshow from the National High Magnetic Field Laboratory)
• NASA page on the 1976 Standard Atmosphere
• Source code and equations for the 1976 Standard Atmosphere
• A mathematical model of the 1976 U.S. Standard Atmosphere
• Calculator using multiple units and properties for the 1976 Standard Atmosphere
• Calculator giving standard air pressure at a specified altitude, or altitude at which a pressure would be standard
• Some of the effects of air pressure

Experiments

• Movies on atmospheric pressure experiments from Georgia State University's HyperPhysics website - requires QuickTime