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Three dimensional extent of an object m 3: L 3: extensive, scalar Volumetric flow rate: Q: Rate of change of volume with respect to time m 3 ⋅s −1: L 3 T −1: extensive, scalar Wavelength: λ: Perpendicular distance between repeating units of a wave m L: Wavenumber: k: Repetency or spatial frequency: the number of cycles per unit distance ...
In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [7] Half of any such diameter may be called a semidiameter, although this term is most often a synonym for the radius of a circle or sphere. [8] The longest diameter is called the ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
optics, photography (ratio of focal length to diameter of aperture) Fresnel number: F = Augustin-Jean Fresnel: optics (slit diffraction) [6] Refractive index: n = electromagnetism, optics (speed of light in vacuum over speed of light in a material) Transmittance: T
d is the characteristic length, e.g. the diameter of the particle (SI units: m). [1] Alternative forms of this number do exist depending on the approach by which Darcy's Law is made dimensionless and the geometry of the system. [2] The Darcy number is commonly used in heat transfer through porous media. [3]
The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number, which prefers a single variable for flow analysis rather than the set of variables as listed in the table below. The Manning formula contains a quantity called the hydraulic radius.
A simple application of dimensional analysis to mathematics is in computing the form of the volume of an n-ball (the solid ball in n dimensions), or the area of its surface, the n-sphere: being an n-dimensional figure, the volume scales as x n, while the surface area, being (n − 1)-dimensional, scales as x n−1.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...