Area density

The area density (also known as areal density, surface density, superficial density, column density, or density thickness) of a two-dimensional object is defined as the quotient of mass by area. The SI derived unit is the "kilogram per square metre" (unit symbol kg·m −2 ). In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (g/m 2 ); for paper in particular, it may be expressed as pounds per ream of standard sizes ("basis ream"). A generalized areic quantity is defined as the quotient of a generic physical quantity by area, such as surface charge density or areic electric charge. A related area number density can be defined by replacing mass by number of particles or other countable quantity.

The area density (also known as areal density, surface density, superficial density, column density, or density thickness) of a two-dimensional object is defined as the quotient of mass by area. The SI derived unit is the "kilogram per square metre" (unit symbol kg·m −2 ). In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (g/m 2 ); for paper in particular, it may be expressed as pounds per ream of standard sizes ("basis ream"). A generalized areic quantity is defined as the quotient of a generic physical quantity by area, such as surface charge density or areic electric charge. A related area number density can be defined by replacing mass by number of particles or other countable quantity. \rho_A = \frac {m} {A} or \rho_A = \rho \cdot l, where is the average area density, is the total mass of the object, is the total area of the object, is the average density, and is the average thickness of the object. \sigma=\int \rho \, \mathrm{d}s. 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: \sigma = \int \rho \, \mathrm{d}z, where z denotes the vertical coordinate (e.g., height or depth). Columnar density \rho_A is closely related to the vertically averaged volumetric density \bar{\rho} as \bar{\rho} = \frac{\rho_A}{\Delta z}, where \Delta z = \int 1 \, \mathrm{d}z ; \bar{\rho} , \rho_A , and \Delta z 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, such as the Total Ozone Mapping Spectrometer (TOMS), which retrieves ozone columns around the globe. Columns are also returned by the differential optical absorption spectroscopy (DOAS) method and are a common retrieval product from nadir-looking microwave radiometers. 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, so the two are related: P = \frac{\sigma}{\rho_0}. Another closely related concept is optical depth. \sigma = \int \rho \, \mathrm{d}z, where z 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): N = \int n \, \mathrm{d}z. ===Data storage media=== Areal density is used to quantify and compare different types media used in data storage devices such as hard disk drives, optical disc drives and tape drives. The current unit of measure is typically gigabits per square inch. ===Paper=== The area density is often used to describe the thickness of paper; e.g., 80 g/m 2 is very common. ===Fabric=== Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or ounces 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 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 −2 ) 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. ==Generalization: areic quantities== The qualifier areic is recommended in the International System of Quantities (ISO 80000-1) to denote the quotient of any physical quantity by area. The expressions "per unit area" or "surface ... density" (or simply "density") are also often used, with resulting units involving reciprocal square metre (m −2 ), for example: surface mass density or areic mass volume per area or areic volume, as in rainfall surface charge density or areic electric charge, electric charge per unit area surface current density or areic electric current, the quotient of electric current to area surface magnetic flux density or areic magnetic flux surface activity density or areic activity heat flow rate density or areic heat flow rate surface power density, power per unit area specific surface energy, free energy per unit surface are ==See also== Linear density Paper density ==References==

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