Просмотр кода страницы Английская Википедия:Area density

{{Английская Википедия/Панель перехода}}
{{short description|Mass per unit area}}
{{About|the property of two-dimensional objects|other uses|Density (disambiguation)}}
{{Infobox physical quantity
| name = Area density
| width =
| background =
| image = 
| caption = 
| unit = kg/m<sup>2</sup>
| otherunits =
| symbols = <math>\rho_A</math>
| baseunits = m<sup>−2</sup>⋅kg
| dimension = wikidata
| extensive =
| intensive =
| conserved =
| transformsas =
| derivations = {{ublist|
|<math>\rho_A = \frac {m} {A}</math>
|<math>\rho_A = \rho l</math>
}}
}}

The '''area density''' (also known as '''areal density''', '''surface density''', '''superficial density''', '''areic density''', '''mass thickness''', '''column density''', or '''density thickness''') of a two-dimensional object is calculated as the [[mass]] per unit [[area]]. The [[SI derived unit]] is the [[kilogram]] per [[square metre]] (kg·m<sup>−2</sup>). 
A related ''[[area number density]]'' can be defined by replacing mass in by [[number of particles]] or other [[countable quantity]].

In the paper and fabric industries, it is called [[grammage]] and is expressed in grams per square meter (g/m<sup>2</sup>); for paper in particular, it may be expressed as pounds per [[paper ream|ream]] of standard sizes ("basis ream").

== Formulation ==
Area density can be calculated as:
<math display="block"> \rho_A = \frac {m} {A} </math>
or
<math display="block"> \rho_A = \rho \cdot l,</math>
where ''{{math|ρ<sub>A</sub>}}'' is the average area density, ''{{math|m}}'' is the total mass of the object, ''{{math|A}}'' is the total area of the object, ''{{math|ρ}}'' is the average [[density]], and ''{{math|l}}'' is the average thickness of the object.

== Column density ==
A special type of area density is called ''column density'' (also ''columnar mass density'' or simply ''column density''), denoted ''ρ''<sub>A</sub> or ''σ''. It is the [[mass]] of [[chemical substance|substance]] per unit [[area]] [[integral|integrated]] along a path;<ref name="Boeker_vanGrondelle2000">
{{cite book
 |author1=Egbert Boeker |author2=Rienk van Grondelle | title=Environmental Physics 
 | edition=2nd
 | year=2000
 | publisher=Wiley
}}</ref> It is obtained integrating [[density|volumetric density]] <math>\rho</math> over a column:<ref>{{Cite book  | last1 = Visconti | first1 = Guido | title = Fundamentals of physics and chemistry of the atmosphere | year = 2001 | publisher = Springer | location = Berlin  | isbn = 978-3-540-67420-7 | pages = 470 }}</ref>
<math display="block">\sigma=\int \rho \, \mathrm{d}s.</math>

In general the integration path can be slant or oblique incidence (as in, for example, [[line of sight propagation]] in [[atmospheric physics]]). A common special case is a vertical path, from the bottom to the top of the medium:
<math display="block">\sigma = \int \rho \, \mathrm{d}z,</math>
where <math>z</math> denotes the vertical coordinate (e.g., height or depth).

Columnar density <math>\rho_A</math> is closely related to the vertically averaged volumetric density <math>\bar{\rho}</math> as
<math display="block">\bar{\rho} = \frac{\rho_A}{\Delta z},</math>
where <math display="inline">\Delta z = \int 1 \, \mathrm{d}z</math>; <math>\bar{\rho}</math>, <math>\rho_A</math>, and <math>\Delta z</math> have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively.

==Usage==

===Atmospheric physics===
It is a quantity commonly retrieved by [[remote sensing]] instruments, for instance the [[Total Ozone Mapping Spectrometer]] (TOMS) which retrieves ozone columns around the globe.  Columns are also returned by the [[differential absorption spectroscopy|differential optical absorption spectroscopy (DOAS)]] method<ref name="Sinreich_etal2008">
{{cite news
 |author1=R. Sinreich |author2=U. Frieß |author3=T. Wagner |author4=S. Yilmaz |author5=U. Platt | title=Retrieval of Aerosol Distributions by Multi-Axis Differential Absorption Spectroscopy (MAX-DOAS)
 | journal=Nucleation and Atmospheric Aerosols
 | year=2008
 | pages= 1145–1149
 | doi=10.1007/978-1-4020-6475-3_227
|isbn=978-1-4020-6474-6 }}</ref> and are a common retrieval product from [[nadir]]-looking [[microwave]] [[radiometers]].<ref name="Melseimer_Heygster2008">
{{cite journal
 |author1=C. Melsheimer |author2=G. Heygster | year=2008
 | title=Improved retrieval of total water vapor over polar regions from [[Advanced Microwave Sounding Unit|AMSU]]-B microwave radiometer data
 | journal=IEEE Trans. Geosci. Remote Sens.
 | volume=46
 | number=8
 | pages=2307–2322
 | doi=10.1109/TGRS.2008.918013
|bibcode = 2008ITGRS..46.2307M |s2cid=20910677 }}</ref><ref name="Melseimer_etal2009">
{{cite news
 |author1=C. Melsheimer |author2=G. Heygster |author3=N. Mathew |author4=L. Toudal Pedersen | year=2009
 | title=Retrieval of Sea Ice Emissivity and Integrated Retrieval of Surface and Atmospheric Parameters over the Arctic from [[AMSR]]-E data| journal=Journal of the Remote Sensing Society of Japan | volume=29
 | number=1
 | pages= 236–241
}}</ref>

A closely related concept is that of ice or [[liquid water path]], which specifies the volume per unit area or depth instead of mass per unit area, thus the two are related:
<math display=block>P = \frac{\sigma}{\rho_0}.</math>

Another closely related concept is [[optical depth]].

===Astronomy===
{{expand section|date=August 2015}}

In astronomy, the column density is generally used to indicate the number of atoms or molecules per square cm (cm<sup>2</sup>) along the line of sight in a particular direction, as derived from observations of e.g. the 21-cm [[hydrogen line]] or from observations of a certain molecular species. Also the [[Extinction (astronomy)|interstellar extinction]] can be related to the column density of H or H<sub>2</sub>.<ref>{{Cite web|url=http://astronomy.swin.edu.au/cosmos/C/Column+Density|title = Column Density &#124; COSMOS}}</ref>

The concept of area density can be useful when analysing [[accretion disk]]s. In the case of a disk seen face-on, area density for a given area of the disk is defined as column density: that is, either as the [[mass]] of [[chemical substance|substance]] per unit [[area]] [[integral|integrated]] along the vertical path that goes through the disk [[Sightline|(line-of-sight)]], from the bottom to the top of the medium:

<math display=block>\sigma = \int \rho \, \mathrm{d}z,</math>

where <math>z</math> denotes the vertical coordinate (e.g., height or depth), or as the number or count of a substance—rather than the mass—per unit area integrated along a path (column number density):

<math display=block>N = \int n \, \mathrm{d}z.</math>

===Data storage media===
{{Main article|Areal density (computer storage)}}
Areal density is used to quantify and compare different types media used in data storage devices such as [[hard disk drives]], [[optical disc|optical disc drives]] and [[tape drives]].  The current unit of measure is typically gigabits per square inch.<ref>{{cite web |url=http://www.webopedia.com/TERM/A/areal_density.html |title=Areal Density |date=3 March 1997 |publisher=Webopedia |access-date= April 9, 2014}}</ref>

===Paper===
{{main|grammage}}
The area density is often used to describe the thickness of paper; e.g., 80&nbsp;g/m<sup>2</sup> is very common.

===Fabric===
{{main|grammage}}
Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or [[ounce]]s per square yard. It is also sometimes specified in ounces per yard in a standard width for the particular cloth. One gram per square meter equals 0.0295 ounces per square yard; one ounce per square yard equals 33.9 grams per square meter.

===Other===

It is also an important quantity for the [[Absorption (electromagnetic radiation)|absorption of radiation]]. 

When studying bodies falling through air, area density is important because resistance depends on area, and gravitational force is dependent on mass.

[[Bone density]] is often expressed in grams per square centimeter (g·cm<sup>−2</sup>) as measured by x-ray absorptiometry, as a proxy for the actual density.

The [[body mass index]] is expressed in units of kilograms per square meter, though the area figure is nominal, being the square of the height.

The [[total electron content]] in the ionosphere is a quantity of type columnar number density.

[[Snow water equivalent]] is a quantity of type columnar mass density.

==See also==
* [[Areic quantity]]
* [[Linear density]]
* [[Paper density]]

==References==
<references/>

{{DEFAULTSORT:Area Density}}
[[Category:Atmospheric physics]]
[[Category:Mass density]]
[[Category:Classical mechanics]]
[[Category:Area-specific quantities]]
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