# Dimensional Analysis

In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions (usually length, mass, time, electric current, temperature, amount of substance and luminous intensity) which describe it; for example, speed has the dimension length per time, and may be measured in meters per second, miles per hour, or other units. Dimensional analysis is based on the fact that a physical law must be independent of the units used to measure the physical variables. A straightforward practical consequence is that any meaningful equation (and any inequality and inequation) must have the same dimensions in the left and right sides. Checking this is the basic way of performing dimensional analysis.

Dimensional analysis is routinely used to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena, and to categorize types of physical quantities and units based on their relations to or dependence on other units, or their dimensions if any.

### Other articles related to "dimensional analysis, analysis, dimensional":

Dimensional Analysis - Dimensional Equivalences - Natural Units
... If c = ħ = 1, where c = luminal speed and ħ = Planck's reduced constant, and a suitable fixed unit of energy is chosen, then all quantities of length L, mass M and time T can be expressed (dimensionally) as a power of energy E, because length, mass and time can be expressed using speed v, action S, and energy E though speed and action are dimensionless (v = c = 1 and S = ħ = 1) — so the only remaining quantity with dimension is energy ... In terms of powers of dimensions This particularly useful in particle physics and high energy physics, in which case the energy unit is the electron volt (eV) ...
Interferometry - Applications - Engineering and Applied Science
... The emergent beam is recorded by an imaging system for analysis ... several issues associated with the classical analysis of static interferograms ... the location of the fringe centers provide the inherent limit to precision of the classical analysis, and any intensity variations across the interferogram will ...
Rayleigh's Method Of Dimensional Analysis
... Rayleigh's method of dimensional analysis is a conceptual tool used in physics, chemistry, and engineering ... This form of dimensional analysis expresses a functional relationship of some variables in the form of an exponential equation ... By using dimensional homogeneity, obtain a set of simultaneous equations involving the exponents a, b, c.. ...
Cobb–Douglas Production Function - Difficulties and Criticisms - Dimensional Analysis
... by some Austrian economists, such as William Barnett II, on the basis of dimensional analysis ...

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