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A special type of area density is called column density (also columnar mass density or simply column density), denoted ρ A or σ. It is the mass of substance per unit area integrated along a path; [ 1 ] It is obtained integrating volumetric density ρ {\displaystyle \rho } over a column: [ 2 ] σ = ∫ ρ d s . {\displaystyle \sigma =\int \rho ...
In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density ...
The density is determined by weighing the sample in air and then in a liquid of known density. Application of Archimedes’ principle leads to the following expression for the measured density of the sample in terms of measured weight, where subscripts “a” and “L” refer to water and liquid, respectively: [ 5 ]
Floor area ratio (FAR) is the ratio of a building's total floor area (gross floor area) to the size of the piece of land upon which it is built. It is often used as one of the regulations in city planning along with the building-to-land ratio. [ 1 ]
If the sides of the cube were multiplied by 2, its surface area would be multiplied by the square of 2 and become 24 m 2. Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the ...
The board foot or board-foot is a unit of measurement for the volume of lumber in the United States and Canada. [1] It equals the volume of a board that is one foot (30.5 cm) in length, one foot in width, and one inch (2.54 cm) in thickness, or exactly 2.359 737 216 liters.
where is the void ratio, is the porosity, V V is the volume of void-space (gases and liquids), V S is the volume of solids, and V T is the total (or bulk) volume. This figure is relevant in composites , in mining (particular with regard to the properties of tailings ), and in soil science .
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...