formulasearchengine - User contributions [en]

Center of percussion

2014-05-27T13:06:43Z

145.94.181.196: /* Further explanation */

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Crocco's theorem

2014-01-01T15:36:48Z

145.94.181.131:

In [[adaptive optics]], the '''Greenwood frequency'''<ref>{{cite journal|last=Greenwood|first=Darryl P.|title=Bandwidth specification for adaptive optics systems|journal=Journal of the Optical Society of America|year=1977|month=March|volume=67|issue=3|pages=390–303|doi=10.1364/JOSA.67.000390|url=http://www.astro.uu.nl/~werkhvn/study/Y5_07_08/master/papers/1977JOSA...67..390G.pdf|bibcode=1977JOSA...67..390G}}</ref> is the frequency or [[Bandwidth (signal processing)|bandwidth]] required for optimal correction with an adaptive optics system. It depends on the [[transverse]] windspeed and the turbulence strength in the atmosphere. This can be easily understood since if the turbulence moves over the telescope opening faster, the speed at which the [[wavefront]] needs to be corrected is higher, and vice-versa. There are various ways to define the Greenwood frequency, but all the definitions attempt to represent the frequency at which the turbulence distortion of the image is changing. The [[Multiplicative inverse|reciprocal]] of the Greenwood frequency is sometimes known as the Greenwood or atmospheric time constant (τ0). Since the distortions are approximately constant over a period less than this time constant, adapting the optical system at a faster rate yields negligible benefits; conversely, adaptive system performance degrades significantly as the response speed decreases below the Greenwood value, since that means that the distortions are changing faster than the system can adapt. Greenwood frequencies in common applications typically run from tens of [[hertz]] up to hundreds or even a few kilohertz, but unusual atmospheric conditions or unusual optical equipment can give very different values.

One expression for the Greenwood frequency is given by

<math>
f_{\mathrm G} = 2.31 \, \lambda^{-6/5} \left[ \sec \zeta \int_{\mathrm{Path}} C_n^2(z) \, v_{\mathrm{Wind}}(z)^{5/3} \, dz \right]^{3/5}
</math><ref>{{cite book|last=Tyson|first=Robert K.|title=Field guide to adaptive optics|year=2004|publisher=SPIE Press|coauthors=Frazier, Benjamin W.|url=http://www.slac.stanford.edu/spires/find/books/www?key=343315|page=14|isbn=0-8194-5319-6}}</ref>

With <math>\zeta</math> the [[zenith]] angle, <math>v_{\mathrm{Wind}}(z)</math> the windspeed as function of height and <math>C_n^2(z)</math> the so-called atmospheric turbulence constant structure function, a measure of the turbulence strength as function of height.

== See also ==
* [[Astronomical seeing]]
* [[Fried parameter]]
* [[Adaptive optics]]

==References==
{{reflist}}

[[Category:Astronomical imaging]]
[[Category:Turbulence]]

Lovász number

2013-12-18T08:28:00Z

145.94.194.223:

The '''Lucas aggregate supply function''' or '''Lucas 'surprise' supply function''', based on the '''Lucas imperfect information model''', is a representation of [[aggregate supply]] based on the work of [[New classical macroeconomics|new classical]] economist [[Robert Lucas, Jr.|Robert Lucas]]. The model states that [[economic output]] is a function of money or price "surprise." The model accounts for the empirically based trade off between output and prices represented by the [[Phillips curve]], but the function breaks from the Phillips curve since only unanticipated price level changes lead to changes in output. The model accounts for empirically observed short-run correlations between output and prices, but maintains the [[neutrality of money]] (the absence of a price or money supply relationship with output and employment) in the long-run. The [[Policy Ineffectiveness Proposition|policy ineffectiveness proposition]] extends the model by arguing that, since people with [[rational expectations]] cannot be systematically surprised by [[monetary policy]], monetary policy cannot be used to systematically influence the economy.

== Background ==
New classical made its first attempt to model aggregate supply in Lucas and [[Leonard Rapping]] (1969).<ref>Snowdon and Vane (2005), 233.</ref> In this earlier model, supply (specifically labor supply) is a direct function of real wages: More work will be done when real wages are high and less when they are low. Under this model, unemployment is "voluntary."<ref>Snowdon and Vane (2005), 233.</ref> In 1972 Lucas made a second attempt at modelling aggregate demand.<ref>Snowdon and Vane (2005), 233.</ref> This attempt drew from [[Milton Friedman]]'s [[natural rate hypothesis]] that challenged the Phillips curve.<ref>Snowdon and Vane (2003), 453.</ref> Lucas supported his original, theoretical paper that outlined the surprise based supply curve with an empirical paper that demonstrated that countries with a history of stable price levels exhibit larger effects in response to monetary policy than countries where prices have been volatile.<ref>Snowdon and Vane, 453.</ref>

Lucas's model dominated new classical economic business cycle theory until 1982 when [[real business cycle theory]] replaced Lucas's theory of a money driven business cycle with a strictly supply based model that used technology and other real shocks to explain fluctuations in output.<ref>Snowdon and Vane (2005), 295.</ref>

== Theory ==
The rationale behind Lucas's supply theory centers on how suppliers get information. Lucas claimed that suppliers had to respond to a "signal extraction" problem when making decisions based on prices; the firms had to determine what portion of price changes in their respective industries reflected a general change in nominal prices (inflation) and what portion reflected a change in real prices for inputs and outputs.<ref>Snowdon and Vane, 233-234.</ref> Lucas hypothesized that suppliers know their own industries better than the general economy. Given this imbalance in information, a supplier could perceive a general increase in prices due to inflation as an increase the [[relative price]] for its output, reflecting a better, real price for its output and encouraging more production. The surprise leads to an increase in production and employment throughout the economy.<ref>Snowdon and Vane (2005), 233-234.</ref>

The function can be represented simply as:

:<math>Y_s = f(P-P_{expected})</math>

The simple version models aggregate output as a function of the price surprise. A more complicated expression of the Lucas supply curve adds expectations to the model. Aggregate supply is a function of the natural level of output(<math>Y_{N_t}</math>) and the difference between actual prices (<math>P_t</math>) and the expected price level given past information <math>\Omega_{t-1}</math> times a coefficient based on an economy's sensitivity to price surprises (<math>\alpha</math>):<ref>Snowdon and Vane (2005), 234.</ref>
:<math>Y_s = Y_{N_t} + \alpha [ P_t - E\left(P_t | \Omega_{t-1} \right) ] </math>

By invoking [[Okun's law]] to express the function in terms of unemployment, Lucas's supply function can be viewed as an expression of the expectations-augmented Phillips curve.<ref>Snowdon and Vane (2005), 235.</ref>

== See also ==
* [[Lucas islands model]]

==References==
* {{cite book | last = Snowdon | first = Brian | coauthors= Howard R. Vane | title = An Encyclopedia of Macroeconomics | publisher = E. Elgar| location = Aldershot | year = 2002 | isbn = 978-1-84542-180-9 }}
* {{cite book | last = Snowdon | first = Brian | coauthors = Howard R. Vane | title = Modern Macroeconomics | publisher = E. Elgar | location = Cheltenham | year = 2005 | isbn = 978-1-84542-208-0 }}

==Citations==
{{reflist}}

[[Category:New classical macroeconomics]]

Flywheel

2013-11-18T11:36:12Z

145.94.177.165: /* Physics */

{{Use mdy dates|date=January 2012}}
{| align="right" border="1" cellspacing="0" cellpadding="2" style="margin: 0 0 0 0.5em; background: #FFFFFF; border-collapse: collapse; border-color: #AAAAAA;"
! {{chembox header}} | Water vapor (H2O)
|-
| colspan="2" align="center"|[[File:St Johns Fog.jpg|250 px]] Invisible water vapor condenses to form visible [[cloud]]s of liquid water droplets
|-
| [[Systematic name]]
| Water vapor
|-
| [[Liquid State]]
| [[Properties of water|water]]
|-
| Solid state
| [[ice]]
|-
! {{chembox header}} | Properties<ref>Lide, David. '' CRC Handbook of Chemistry and Physics, 73rd ed''. 1992, CRC Press.</ref>
|-
| [[Chemical formula|Molecular formula]]
| H2O
|-
| [[Molar mass]]
| 18.01528(33) g/mol
|-
| [[Melting point]]
| {{convert|0.00|C|K}}<ref name="VSMOW">[[Vienna Standard Mean Ocean Water]] (VSMOW), used for calibration, melts at 273.1500089(10) K (0.000089(10) °C, and boils at 373.1339 K (99.9839 °C)</ref>
|-
| [[Boiling point]]
| {{convert|99.98|C|K}}<ref name="VSMOW" />
|-
| [[Gas constant#Specific gas constant|specific gas constant]]
| 461.5 J/(kg·K)
|-
| [[Heat of vaporization]]
| 2.27 MJ/kg
|-
| [[Heat capacity]] at 300 K
| 1.864 kJ/(kg·K)<ref>{{Cite web
| title = Water Vapor - Specific Heat
| url = http://www.engineeringtoolbox.com/water-vapor-d_979.html
| accessdate = May 15, 2012
}}</ref>
|-
|}

'''Water vapor''' or '''aqueous vapor''' is the [[gas]] phase of [[Properties of water|water]]. It is one [[Phase (matter)|state]] of water within the [[hydrosphere]]. Water [[vapor]] can be produced from the [[evaporation]] or [[boiling]] of liquid water or from the [[Sublimation (phase transition)|sublimation]] of [[ice]]. Unlike other forms of water, water vapor is invisible.<ref>{{cite web|title=What is Water Vapor?|url=http://www.weatherquestions.com/What_is_water_vapor.htm|accessdate=2012-08-28}}</ref> Under typical atmospheric conditions, water vapor is continuously generated by evaporation and removed by [[condensation]]. It is lighter than air and triggers [[convection]] currents that can lead to clouds.

Water vapor is a potent [[greenhouse gas]] along with other gases such as [[carbon dioxide]] and [[methane]].

== General properties of water vaporization ==

=== Evaporation and sublimation ===
Whenever a water molecule leaves a surface and diffuses into a surrounding gas, it is said to have [[Evaporation|evaporated]]. Each individual water molecule which transitions between a more associated (liquid) and a less associated (vapor/gas) state does so through the absorption or release of kinetic energy. The aggregate measurement of this kinetic energy transfer is defined as thermal energy and occurs only when there is differential in the temperature of the water molecules. Liquid water that becomes water vapor takes a parcel of heat with it, in a process called [[evaporative cooling]].<ref>Schroeder, David. ''Thermal Physics''. 2000, Addison Wesley Longman. p36</ref> The amount of water vapor in the air determines how fast each molecule will return to the surface. When a net evaporation occurs, the body of water will undergo a net cooling directly related to the loss of water.

In the US, the National Weather Service measures the actual rate of evaporation from a standardized "pan" open water surface outdoors, at various locations nationwide. Others do likewise around the world. The US data is collected and compiled into an annual evaporation map.<ref>http://www.grow.arizona.edu/Grow--GrowResources.php?ResourceId=208{{dead link|date=May 2013}}</ref> The measurements range from under 30 to over 120 inches per year. Formulas can be used for calculating the rate of evaporation from a water surface such as a swimming pool.<ref>[http://www.thermexcel.com/english/program/pool.htm swimming, pool, calculation, evaporation, water, thermal, temperature, humidity, vapor, excel]</ref><ref>http://www.rlmartin.com/rspec/whatis/equations.htm{{dead link|date=May 2013}}</ref> In some countries, the evaporation rate far exceeds the [[Precipitation (meteorology)|precipitation]] rate.

Evaporative cooling is restricted by [[Standard conditions for temperature and pressure|atmospheric conditions]]. [[Humidity]] is the amount of water vapor in the air. The vapor content of air is measured with devices known as [[hygrometer]]s. The measurements are usually expressed as [[specific humidity]] or percent [[relative humidity]]. The temperatures of the atmosphere and the water surface determine the equilibrium vapor pressure; 100% relative humidity occurs when the partial pressure of water vapor is equal to the equilibrium vapor pressure. This condition is often referred to as complete saturation. Humidity ranges from 0 gram per cubic metre in dry air to 30 grams per cubic metre (0.03 ounce per cubic foot) when the vapor is saturated at 30 °C.<ref>[http://www.britannica.com/eb/article-53259/climate#292984.hook climate (meteorology) - Encyclopedia Britannica]</ref>
(See also [http://www.tis-gdv.de/tis_e/misc/klima.htm Absolute Humidity table])
[[File:Meteorite Recovery Antarctica.jpg|thumb|left|Meteorite Recovery Antarctica]]
[[File:Tightjunction BBB.jpg|thumb|Electron micrograph of tight junctions in blood–brain barrier, prepared by sublimation in freeze-etching process.]]

Another form of evaporation is [[Sublimation (phase transition)|sublimation]], by which water molecules become gaseous directly, leaving the surface of ice without first becoming liquid water. Sublimation accounts for the slow mid-winter disappearance of ice and snow at temperatures too low to cause melting. [[Antarctica]] shows this effect to a unique degree because it is by far the continent with the lowest rate of precipitation on Earth. As a result there are large areas where [[Millennium|millennial]] layers of snow have sublimed, leaving behind whatever non-volatile materials they had contained. This is extremely valuable to certain scientific disciplines, a dramatic example being the collection of [[meteorite]]s that are left exposed in unparalleled numbers and excellent states of preservation.

Sublimation is of importance in the preparation of certain classes of biological specimens for [[Scanning electron microscope|scanning electron microscopy]]. Typically the specimens are prepared by [[cryofixation]] and [[Electron microscope|freeze-fracture]], after which the broken surface is freeze-etched, being eroded by exposure to vacuum till it shows the required level of detail. This technique can display protein molecules, [[organelle]] structures and [[lipid bilayer]]s with very low degrees of distortion.

=== Condensation ===
[[Image:Above the Clouds.jpg|thumb|right|200px|Clouds, formed by condensed water vapor.]]
Water vapor will only condense onto another surface when that surface is cooler than the [[dew point]] temperature, or when the [[saturation vapor pressure|water vapor equilibrium]] in air has been exceeded. When water vapor condenses onto a surface, a net warming occurs on that surface. The water molecule brings heat energy with it. In turn, the temperature of the atmosphere drops slightly.<ref>Schroeder, p19.</ref> In the atmosphere, condensation produces clouds, fog and precipitation (usually only when facilitated by [[cloud condensation nuclei]]). The [[dew point]] of an air parcel is the temperature to which it must cool before water vapor in the air begins to condense.

Also, a net condensation of water vapor occurs on surfaces when the temperature of the surface is at or below the dew point temperature of the atmosphere. Deposition, the direct formation of ice from water vapor, is a type of condensation. [[Frost]] and snow are examples of [[Deposition (meteorology)|deposition]].

===Chemical reactions===
A number of chemical reactions have water as a product. If the reactions take place at temperatures higher than the dew point of the surrounding air the water will be formed as vapor and increase the local humidity, if below the dew point local condensation will occur. Typical reactions that result in water formation are the burning of [[hydrogen]] or many other [[hydrocarbon]]s in air itself or in combination with [[oxygen]] or other oxidisers.

In a similar fashion other chemical or physical reactions can take place in the presence of water vapor resulting in new chemicals forming such as [[rust]] on iron or steel, polymerisation occurring (certain [[polyurethane]] foams and [[cyanoacrylate]] glues cure with exposure to atmospheric humidity) or forms changing such as where anhydrous chemicals may absorb enough vapor to form a crystalline structure or alter an existing one, sometimes resulting in characteristic color changes that can be used for [[humidity indicator card|measurement]].

===Measurement===
Measuring the quantity of water vapor in a medium can be done directly or remotely with varying degrees of accuracy. Remote methods such electromagnetic absorption are possible from satellites above planetary atmospheres. Direct methods may use electronic transducers, moistened thermometers or hygroscopic materials measuring changes in physical properties or dimensions.

{| class="wikitable sortable" style="text-align: center; font-size: 85%; width: auto; table-layout: fixed;"

! style="width:12em" |
! medium
! temperature range (degC)
! measurement [[Measurement uncertainty|uncertainty]]
! typical measurement frequency
! system cost
! notes
|-
! style="text-align:left;" | sling psychrometer
| air
| −10 to 50
| low to moderate
| hourly
| low
|
|-
! style="text-align:left;" | satellite-based spectroscopy
| air
| −80 to 60
| low
|
| very high
|
|-
! style="text-align:left;" | capacitive sensor
| air/gases
| −40 to 50
| moderate
| 2 to 0.05 Hz
| medium
| prone to becoming saturated/contaminated over time
|-
! style="text-align:left;" | warmed capacitive sensor
| air/gases
| −15 to 50
| moderate to low
| 2 to 0.05 Hz (temp dependant)
| medium to high
| prone to becoming saturated/contaminated over time
|-
! style="text-align:left;" | resistive sensor
| air/gases
| −10 to 50
| moderate
| 60 seconds
| medium
| prone to contamination
|-
! style="text-align:left;" | lithium chloride [[dewcell]]
| air
| −30 to 50
| moderate
| continuous
| medium
| see [[dewcell]]
|-
! style="text-align:left;" | [[Cobalt(II) chloride]]
| air/gases
| 0 to 50
| high
| 5 minutes
| very low
| often used in [[Humidity indicator card]]
|-
! style="text-align:left;" | [[Absorption spectroscopy]]
| air/gases
|
| moderate
|
| high
|
|-
! style="text-align:left;" | Aluminum oxide
| air/gases
|
| moderate
|
| medium
| see [[Moisture analysis]]
|-
! style="text-align:left;" | silicon oxide
| air/gases
|
| moderate
|
| medium
| see [[Moisture analysis]]
|-
! style="text-align:left;" | Piezoelectric sorption
| air/gases
|
| moderate
|
| medium
| see [[Moisture analysis]]
|-
! style="text-align:left;" | Electrolytic
| air/gases
|
| moderate
|
| medium
| see [[Moisture analysis]]
|-
! style="text-align:left;" | hair tension
| air
| 0 to 40
| high
| continuous
| low to medium
| Affected by temperature. Adversely affected by prolonged high concentrations
|-class="sortbottom"
|-
! style="text-align:left;" | Nephelometer
| air/other gases
|
| low
|
| very high
|
|-
! style="text-align:left;" | Goldbeater's skin (cow Peritoneum)
| air
| −20 to 30
| moderate (with corrections)
| slow, slower at lower temperatures
| low
| ref:WMO Guide to Meteorological Instruments and Methods of Observation No. 8 2006, (pages 1.12–1)
|-
! style="text-align:left;" | Lyman-alpha
|
|
|
| high frequency
| high
| http://amsglossary.allenpress.com/glossary/search?id=lyman-alpha-hygrometer1 Requires frequent calibration
|-
! style="text-align:left;" | Gravimetric Hygrometer
|
|
| very low
|
| very high
| often called primary source, national independent standards developed in US,UK,EU & Japan
|-class="sortbottom"
!
! medium
! temperature range (degC)
! measurement [[Measurement uncertainty|uncertainty]]
! typical measurement frequency
! system cost
! notes
|}

===Water vapor density===
Water vapor is lighter or less [[density|dense]] than dry air. At equivalent temperatures it is buoyant with respect to dry air.

====Water vapor and dry air density calculations at 0 °C====
[[Image:dewpoint.jpg|right]]
The [[molar mass]] of water is {{nowrap|18.02 g/mol}}, as calculated from the sum of the [[atomic masses]] of its constituent [[atoms]].

The average molecular mass of air (approx. 79% nitrogen, N2; 21% oxygen, O2) is {{nowrap|28.57 g/mol}} at standard temperature and pressure ([[Standard conditions for temperature and pressure|STP]]).

Using [[Avogadro's Law]] and the [[ideal gas]] law, water vapor and air will have a [[molar volume]] of {{nowrap|22.414 L/mol}} at STP. A molar mass of air and water vapor occupy the same volume of 22.414 litres. The [[density]] (mass/volume) of water vapor is {{nowrap|0.804 g/L}}, which is significantly less than that of dry air at {{nowrap|1.27 g/L}} at STP.

STP conditions imply a temperature of 0 °C, at which the ability of water to become vapor is very restricted. Its [[concentration]] in air is very low at 0 °C. The red line on the chart to the right is the maximum concentration of water vapor expected for a given temperature. The water vapor concentration increases significantly as the temperature rises, approaching 100% ([[steam]], pure water vapor) at 100 °C. However the difference in densities between air and water vapor would still exist.

====Air and water vapor density interactions at equal temperatures====
At the same temperature, a column of dry air will be denser or heavier than a column of air containing any water vapor. Thus, any volume of dry air will sink if placed in a larger volume of moist air. Also, a volume of moist air will rise or be [[Buoyancy|buoyant]] if placed in a larger region of dry air. As the temperature rises the proportion of water vapor in the air increases, and its buoyancy will increase. The increase in buoyancy can have a significant atmospheric impact, giving rise to powerful, moisture rich, upward air currents when the air temperature and sea temperature reaches 25 °C or above. This phenomenon provides a significant motivating force for cyclonic and anticyclonic weather systems (typhoons and hurricanes).

===Water vapor and respiration or breathing===
Water vapor is a by-product of [[respiration (physiology)|respiration]] in plants and animals. Its contribution to the pressure, increases as its concentration increases. Its [[partial pressure]] contribution to air pressure increases, lowering the partial pressure contribution of the other atmospheric gases [[partial pressure|(Dalton's Law)]]. The total air pressure must remain constant. The presence of water vapor in the air naturally dilutes or displaces the other air components as its concentration increases.

This can have an effect on respiration. In very warm air (35 °C) the proportion of water vapor is large enough to give rise to the stuffiness that can be experienced in humid jungle conditions or in poorly ventilated buildings.

===Lifting gas===

Water vapor is a lifting gas when the liquid temperature raises the vapor pressure greater than the surrounding air pressure, due to its low molecular weight. A high enough temperature to maintain a theoretical "steam balloon" yields approximately 60% the lift of helium and twice that of hot air.<ref>{{Cite web
| last = Goodey
| first = Thomas J.
| title = Steam Balloons and Steam Airships
| date =
| url = http://www.flyingkettle.com/jbfa.htm
| accessdate = August 26, 2010
}}</ref>

=== General discussion ===

The amount of water vapor in an atmosphere is constrained by the restrictions of partial pressures and temperature. Dew point temperature and relative humidity act as guidelines for the process of water vapor in the [[water cycle]]. Energy input, such as sunlight, can trigger more evaporation on an ocean surface or more sublimation on a chunk of ice on top of a mountain. The ''balance'' between condensation and evaporation gives the quantity called [[vapor pressure|vapor partial pressure]].

The maximum partial pressure (''saturation pressure'') of water vapor in air varies with temperature of the air and water vapor mixture. A variety of empirical formulas exist for this quantity; the most used reference formula is the [[Goff-Gratch equation]] for the SVP over liquid water below zero degree Celsius:

{| background=#efefef align=center
|
|-
|<math>\log_{10} \left( p \right)= </math>
|<math>-7.90298 \left( \frac{373.16}{T}-1 \right) + 5.02808 \log_{10} \frac{373.16}{T} </math>
|-
|
|<math>- 1.3816 \times 10^{-7} \left( 10^{11.344 \left( 1-\frac{T}{373.16} \right)} -1 \right) </math>
|-
|
|<math>+ 8.1328 \times 10^{-3} \left( 10^{-3.49149 \left( \frac{373.16}{T}-1 \right)} -1 \right) </math>
|-
|
|<math>+ \log_{10} \left( 1013.246 \right)</math>
|}

:Where '''''T''''', temperature of the moist air, is given in units of [[kelvin]]s, and '''''p''''' is given in units of [[millibar]]s ([[hectopascal]]s).
The formula is valid from about −50 to 102 °C; however there are a very limited number of measurements of the vapor pressure of water over supercooled liquid water. There are a number of other formulae which can be used.<ref>[http://cires.colorado.edu/~voemel/vp.html Water Vapor Pressure Formulations]</ref>

Under certain conditions, such as when the boiling temperature of water is reached, a net evaporation will always occur during standard atmospheric conditions regardless of the percent of relative humidity. This immediate process will dispel massive amounts of water vapor into a cooler atmosphere.

[[Exhalation|Exhale]]d air is almost fully at equilibrium with water vapor at the body temperature. In the cold air the exhaled vapor quickly condenses, thus showing up as a fog or [[mist]] of water droplets and as condensation or frost on surfaces. Forcibly condensing these water droplets from exhaled breath is the basis of [[exhaled breath condensate]], an evolving medical diagnostic test.

Controlling water vapor in air is a key concern in the [[HVAC|heating, ventilating, and air-conditioning]] (HVAC) industry. [[Thermal comfort]] depends on the moist air conditions. Non-human comfort situations are called [[refrigeration]], and also are affected by water vapor. For example many food stores, like supermarkets, utilize open chiller cabinets, or ''food cases'', which can significantly lower the water vapor pressure (lowering humidity). This practice delivers several benefits as well as problems.

==Water vapor in Earth's atmosphere==
[[Image:BAMS climate assess boulder water vapor 2002.gif|thumb|Evidence for increasing amounts of stratospheric water vapor over time in Boulder, Colorado.]]
[[File:MYDAL2 M SKY WV.ogv|thumb|These maps show the average amount of water vapor in a column of atmosphere in a given month. The units are given in centimeters, which is the equivalent amount of water that could be produced if all the water vapor in the column were to condense. The lowest amounts of water vapor (0 centimeters) appear in yellow, and the highest amounts (6 centimeters) appear in dark blue. Areas of missing data appear in shades of gray. The maps are based on data collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on NASA’s Aqua satellite. The most noticeable pattern in the time series is the influence of seasonal temperature changes and incoming sunlight on water vapor. In the tropics, a band of extremely humid air wobbles north and south of the equator as the seasons change. This band of humidity is part of the Intertropical Convergence Zone, where the easterly trade winds from each hemisphere converge and produce near-daily thunderstorms and clouds. Farther from the equator, water vapor concentrations are high in the hemisphere experiencing summer and low in the one experiencing winter. Another pattern that shows up in the time series is that water vapor amounts over land areas decrease more in winter months than adjacent ocean areas do. This is largely because air temperatures over land drop more in the winter than temperatures over the ocean. Water vapor condenses more rapidly in colder air. <ref>http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MYDAL2_M_SKY_WV</ref> (''click for more detail'')]]

Gaseous water represents a small but environmentally significant constituent of the [[Earth's atmosphere|atmosphere]]. The percentage water vapor in surface air varies from .01% at -42℃ (-44℉)<ref>Michael B. McElroy "The Atmospheric Environment" 2002 Princeton University Press p. 34 figure 4.3a</ref> to 4.24% when the dew point is 30℃ (86℉).<ref>Michael B. McElroy "The Atmospheric Environment" 2002 Princeton University Press p. 36 example 4.1</ref> Approximately 99.13% of it is contained in the [[troposphere]]. The [[condensation]] of water vapor to the liquid or ice phase is responsible for [[clouds]], rain, snow, and other [[Precipitation (meteorology)|precipitation]], all of which count among the most significant elements of what we experience as weather. Less obviously, the [[latent heat of vaporization]], which is released to the atmosphere whenever condensation occurs, is one of the most important terms in the atmospheric energy budget on both local and global scales. For example, latent heat release in atmospheric [[convection]] is directly responsible for powering destructive storms such as [[tropical cyclones]] and severe [[thunderstorms]]. Water vapor is also the most potent [[greenhouse gas]] owing to the presence of the [[hydroxyl]] bond which strongly absorbs in the [[infra-red]] region of the [[light spectrum]].

Because the water vapor content of the atmosphere will increase in response to warmer temperatures, there is a [[water vapor feedback]] which is expected to amplify the climate warming effect due to increased [[carbon dioxide]] alone. It is less clear how cloudiness would respond to a warming climate; depending on the nature of the response, clouds could either further amplify or partly mitigate warming from long-lived greenhouse gases.

[[Fog]] and clouds form through condensation around [[cloud condensation nuclei]]. In the absence of nuclei, condensation will only occur at much lower temperatures. Under persistent condensation or deposition, cloud droplets or snowflakes form, which [[precipitation (meteorology)|precipitate]] when they reach a critical mass.

The water content of the atmosphere as a whole is constantly depleted by precipitation. At the same time it is constantly replenished by evaporation, most prominently from seas, lakes, rivers, and moist earth. Other sources of atmospheric water include combustion, respiration, volcanic eruptions, the transpiration of plants, and various other biological and geological processes. The mean global content of water vapor in the atmosphere is roughly sufficient to cover the surface of the planet with a layer of liquid water about 25 mm deep. The mean annual precipitation for the planet is about 1 meter, which implies a rapid turnover of water in the air – on average, the residence time of a water molecule in the [[troposphere]] is about 9 to 10 days.

Episodes of surface geothermal activity, such as volcanic eruptions and geysers, release variable amounts of water vapor into the atmosphere. Such eruptions may be large in human terms, and major explosive eruptions may inject exceptionally large masses of water exceptionally high into the atmosphere, but as a percentage of total atmospheric water, the role of such processes is minor. The relative concentrations of the various gases emitted by [[volcano]]es varies considerably according to the site and according to the particular event at any one site. However, water vapor is consistently the commonest [[volcanic gas]]; as a rule, it comprises more than 60% of total emissions during a [[subaerial eruption]].<ref>Sigurdsson, H. et al., (2000) ''Encyclopedia of Volcanoes'', San Diego, Academic Press</ref>

Atmospheric water vapor content is expressed using various measures. These include vapor pressure, [[specific humidity]], mixing ratio, dew point temperature, and [[relative humidity]].

===Radar and satellite imaging===
[[Image:Atmospheric Water Vapor Mean.2005.030.jpg|thumb|[[MODIS]]/[[Terra (satellite)|Terra]] global mean atmospheric water vapor ]]

Because water molecules [[Absorption (electromagnetic radiation)|absorb]] [[microwave]]s and other [[radio wave]] frequencies, water in the atmosphere attenuates [[radar]] signals.<ref>Skolnik, Merrill. ''Radar Handbook, 2nd ed''. 1990, McGraw-Hill, Inc. p23.5</ref> In addition, atmospheric water will [[Reflection (physics)|reflect]] and [[refraction|refract]] signals to an extent that depends on whether it is vapor, liquid or solid.

Generally, radar signals lose strength progressively the farther they travel through the troposphere. Different frequencies attenuate at different rates, such that some components of air are opaque to some frequencies and transparent to others. Radio waves used for broadcasting and other communication experience the same effect.

Water vapor reflects radar to a lesser extent than do water's other two phases. In the form of drops and ice crystals, water acts as a prism, which it does not do as an individual [[molecule]]; however, the existence of water vapor in the atmosphere causes the atmosphere to act as a giant prism.<ref>Skolnik, pp2.44-2.54.</ref>

A comparison of [[GOES-12]] satellite images shows the distribution of atmospheric water vapor relative to the oceans, clouds and continents of the Earth. Vapor surrounds the planet but is unevenly distributed.

===Lightning generation===
Water vapor plays a key role in [[lightning]] production in the atmosphere. From [[cloud physics]], usually, clouds are the real generators of static [[electric charge|charge]] as found in Earth's atmosphere. But the ability, or capability of clouds to hold massive amounts of electrical energy is directly related to the amount of water vapor present in the local system.

The amount of water vapor directly controls the [[permittivity]] of the air. During times of low humidity, static discharge is quick and easy. During times of higher humidity, fewer static discharges occur. Permittivity and capacitance work hand in hand to produce the megawatt outputs of lightning.<ref>Shadowitz, Albert. ''The Electromagnetic Field''. 1975, McGraw-Hill Book Company. pp165-171.</ref>

After a cloud, for instance, has started its way to becoming a lightning generator, atmospheric water vapor acts as a substance (or [[electrical insulation|insulator]]) that decreases the ability of the cloud to [[electrostatic discharge|discharge]] its electrical energy. Over a certain amount of time, if the cloud continues to generate and store more [[static electricity]], the barrier that was created by the atmospheric water vapor will ultimately break down from the stored electrical potential energy.<ref>Shadowitz, pp172-173, 182.</ref><ref>Shadowitz, pp414-416.</ref> This energy will be released to a locally, oppositely charged region in the form of lightning. The strength of each discharge is directly related to the atmospheric permittivity, capacitance, and the source's charge generating ability.<ref>Shadowitz, p172.</ref>

''See also,'' [[Van de Graaff generator]].

=== Extraterrestrial water vapor ===
{{See|Extraterrestrial liquid water}}
[[File:PIA17659-Europa-WaterPlume-ArtistConcept-20131212.jpg|thumb|250px|right|Plume of water vapor on [[Europa (moon)|Europa]] (artist concept) (December 12, 2013).<ref name="NASA-20131212-EU" />]]
The brilliance of comet tails comes largely from water vapor. On approach to the [[sun]], the ice many [[comet]]s carry [[Sublimation (phase transition)|sublimates]] to vapor, which reflects light from the sun. Knowing a comet's distance from the sun, astronomers may deduce a comet's water content from its brilliance.<ref>[http://www.il-st-acad-sci.org/planets/comets3.html ANATOMY OF COMETS], Retrieved December 2006.</ref> Bright tails in cold and distant comets suggests carbon monoxide sublimation.

Plumes of water vapor have been detected on [[Europa (moon)|Europa]]<ref name="NASA-20131212-EU">{{cite web|last1=Cook |first1=Jia-Rui C.|last2=Gutro|first2=Rob|last3=Brown|first3=Dwayne|last4=Harrington |first4=J.D. |last5=Fohn|first5=Joe|title=Hubble Sees Evidence of Water Vapor at Jupiter Moon|url=http://www.jpl.nasa.gov/news/news.php?release=2013-363|date=December 12, 2013 |work=[[NASA]] |accessdate=December 12, 2013 }}</ref> (a moon of Jupiter) and are similar to plumes of water vapor detected on [[Enceladus]]<ref name="NASA-20131212-EU" /> (a moon of Saturn) and in the stratosphere of [[Titan (moon)|Titan]].<ref name="CottiniNixon2012">{{cite journal|last1=Cottini|first1=V.|last2=Nixon|first2=C.A.|last3=Jennings|first3=D.E.|last4=Anderson|first4=C.M.|last5=Gorius|first5=N.|last6=Bjoraker|first6=G.L.|last7=Coustenis|first7=A.|last8=Teanby|first8=N.A.|last9=Achterberg|first9=R.K.|last10=Bézard|first10=B.|last11=de Kok|first11=R.|last12=Lellouch|first12=E.|last13=Irwin|first13=P.G.J.|last14=Flasar|first14=F.M.|last15=Bampasidis|first15=G.|title=Water vapor in Titan’s stratosphere from Cassini CIRS far-infrared spectra|journal=Icarus|volume=220|issue=2|year=2012|pages=855–862|issn=00191035|doi=10.1016/j.icarus.2012.06.014}}</ref>

Scientists studying [[Mars]] hypothesize that if water moves about the planet, it does so as vapor.<ref>Jakosky, Bruce, et al. ''"Water on Mars"'', April 2004, Physics Today, p71.</ref> Most of the water on Mars appears to exist as ice at the northern pole. During Mars' summer, this ice sublimates, perhaps enabling massive seasonal storms to convey significant amounts of water toward the equator.<ref>''"Europe probe detects Mars water ice"'', January 23, 2004, [http://www.cnn.com/2004/TECH/space/01/23/mars.water.ice/index.html Cnn.com], retrieved August 2005.</ref>

A star called [[IRC +10216|CW Leonis]] was found to have a ring of vast quantities of water vapor circling the aging, massive [[star]]. A [[NASA]] satellite designed to study chemicals in interstellar gas clouds, made the discovery with an onboard spectrometer. Most likely, "the water vapor was vaporized from the surfaces of orbiting comets."<ref>Lloyd, Robin. ''"Water Vapor, Possible Comets, Found Orbiting Star"'', 11 July 2001, [http://www.space.com/searchforlife/swas_water_010711.html Space.com]. Retrieved December 15, 2006.</ref>

Spectroscopic analysis of [[HD 209458 b]], an extrasolar planet in the constellation Pegasus, provides the first evidence of atmospheric water vapor beyond the Solar System.

In January 2014, [[European Space Agency|ESA scientists]] reported the detection, for the first definitive time, of water vapor on the [[dwarf planet]], [[Ceres (dwarf planet)|Ceres]], largest object in the [[asteroid belt]].<ref name="KüppersO’Rourke2014">{{cite journal |last1=Küppers |first1=Michael |last2=O’Rourke |first2=Laurence |last3=Bockelée-Morvan |first3=Dominique |last4=Zakharov |first4=Vladimir |last5=Lee |first5=Seungwon |last6=von Allmen |first6=Paul |last7=Carry |first7=Benoît |last8=Teyssier |first8=David |last9=Marston |first9=Anthony |last10=Müller |first10=Thomas |last11=Crovisier |first11=Jacques |last12=Barucci |first12=M. Antonietta |last13=Moreno |first13=Raphael |title=Localized sources of water vapour on the dwarf planet (1) Ceres |journal=Nature |volume=505 |issue=7484 |year=2014 |pages=525–527 |issn=0028-0836 |doi=10.1038/nature12918 }}</ref> The detection was made by using the [[Far-infrared astronomy|far-infrared abilities]] of the [[Herschel Space Observatory]].<ref name="NASA-20140122">{{cite web |last1=Harrington |first1=J.D. |title=Herschel Telescope Detects Water on Dwarf Planet - Release 14-021 |url=http://www.nasa.gov/press/2014/january/herschel-telescope-detects-water-on-dwarf-planet |date=January 22, 2014 |work=[[NASA]] |accessdate=January 22, 2014 }}</ref> The finding is unexpected because [[comets]], not [[asteroids]], are typically considered to "sprout jets and plumes." According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids."<ref name="NASA-20140122" />

==See also==
{{commons|Water vapor|Water vapor}}

{| border="0" cellpadding="5" cellspacing="0"
|-
|
* [[Earth's atmosphere|Air]]
* [[Boiling point]]
* [[Condensation in aerosol dynamics]]
* [[Deposition (meteorology)|deposition]]
* [[Eddy covariance]]
* [[Equation of state]]
* [[Evaporative cooler]]
* [[Fog]]
* [[Frost]]
* [[Gas laws]]
* [[Gibbs free energy]]
||
* [[Gibbs phase rule]]
* [[Greenhouse gas]]
* [[Heat capacity]]
* [[Heat of vaporization]]
* [[Humidity]]
* [[Ideal gas]]
* [[Kinetic theory of gases]]
* [[Latent heat flux]]
* [[Latent heat]]
||
* [[Microwave radiometer]]
* [[Phase (matter)|phase of matter]]
* [[Saturation vapor density]]
* [[Steam]]
* [[Sublimation (phase transition)|sublimation]]
* [[Superheating]]
* [[Supersaturation]]
* [[Thermodynamics]]
* [[Troposphere]]
* [[Vapor pressure]]
|}

{{Meteorological variables}}
{{Water}}

== References ==
{{Reflist|2}}

==External links==
*[http://www.nsdl.arm.gov/Library/glossary.shtml#water_vapor National Science Digital Library – Water Vapor]
*[http://www.sciencebits.com/exhalecondense Calculate the condensation of your exhaled breath]
*[http://www.atmos.umd.edu/~stevenb/vapor/ Water Vapor Myths: A Brief Tutorial]
*[http://www.eso.org/gen-fac/pubs/astclim/espas/pwv/mockler.html AGU Water Vapor in the Climate System – 1995]
*[http://www.phymetrix.com/Software.htm Free Windows Program, Water Vapor Pressure Units Conversion Calculator] – PhyMetrix

{{DEFAULTSORT:Water Vapor}}
[[Category:Greenhouse gases]]
[[Category:Atmospheric thermodynamics]]
[[Category:Forms of water]]
[[Category:Water in gas]]
[[Category:Psychrometrics]]

{{Link FA|de}}
{{Link FA|nn}}

Görtler vortices

2013-10-30T14:42:30Z

145.94.47.123:

'''Red blood cell indices''' are [[blood test]]s that provide information about the [[hemoglobin]] content and size of [[red blood cells]]. Abnormal values indicate the presence of [[anemia]] and which type of anemia it is.<ref>[http://www.nlm.nih.gov/medlineplus/ency/article/003648.htm MedlinePlus Medical Encyclopedia: RBC indices]</ref>

== Mean corpuscular volume ==
{{main|Mean corpuscular volume}}
Mean corpuscular volume (MCV) is the average size of a red blood cell and is calculated by dividing the [[hematocrit]] (Hct) by the red blood cell count.
* <math>MCV = \frac{Hct}{RBC}</math> x 10
* Normal range: 80-100 fL

== Mean corpuscular hemoglobin ==
{{main|Mean corpuscular hemoglobin}}
Mean corpuscular hemoglobin (MCH) is the average amount of [[hemoglobin]] (Hb) per red blood cell and is calculated by dividing the hemoglobin by the red blood cell count.
*<math>MCH = \frac{Hb}{RBC}</math> x 10
*Normal range: 27-31 pg/cell
×

== Mean corpuscular hemoglobin concentration ==
{{main|Mean corpuscular hemoglobin concentration}}
Mean corpuscular hemoglobin concentration (MCHC) is the average concentration of hemoglobin per unit volume of red blood cells and is calculated by dividing the hemoglobin by the hematocrit.
* <math>MCHC = \frac{Hb}{Hct}</math> x 100
* Normal range: 32-36 g/dL

==Worked example==
{{Red blood cell indices worked example}}

== References ==
{{reflist}}

{{Myeloid blood tests}}
[[Category:Blood tests]]

Krasovskii–LaSalle principle

2012-07-23T12:47:16Z

145.94.197.45: /* Example: the pendulum with friction */

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