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| {{Refimprove|date=December 2009}}
| | They call me Mari. Some time ago I decided i would live in Kansas which can never work. Playing handball is what my in addition to I get pleasure. For years I've been working for a production and planning police. Go to her website to find out more: [http://waldob9.blog.com/2014/06/15/reciclaje-funcional-de-la-fibra-de-vidrio/ http://waldob9.blog.com/2014/06/15/reciclaje-funcional-de-la-fibra-de-vidrio/] |
| The '''Archimedes number''' ('''Ar''') (not to be confused with Archimedes' '''constant''', [[pi|π]]), named after the ancient Greek scientist [[Archimedes]] is used to determine the motion of [[fluid]]s due to [[density]] differences. It is a [[dimensionless number]] defined as the ratio of gravitational forces to viscous forces<ref>{{cite web | url=http://scienceworld.wolfram.com/physics/ArchimedesNumber.html | title=Eric Weisstein's World of Physics | accessdate=9 November 2012}}</ref> and has the form:
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| :<math>\mathrm{Ar} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2}</math>
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| where:
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| * ''g'' = [[gravitational acceleration]] (9.81 m/s²),
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| * ρ<sub>''l''</sub> = density of the fluid, <math>{\rm kg/m}^3</math>
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| * ρ = density of the body, <math>{\rm kg/m}^3</math>
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| * <math>\mu</math> = dynamic viscosity, <math>{\rm kg/m s}</math>
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| * L = characteristic length of body, m
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| When analyzing potentially mixed [[convection]] of a liquid, the Archimedes number parametrizes the relative strength of free and [[forced convection]]. When Ar >> 1 natural convection dominates, i.e. less dense bodies rise and denser bodies sink, and when Ar << 1 forced convection dominates.
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| When the density difference is due to heat transfer (e.g. fluid being heated and causing a temperature difference between different parts of the fluid), then we may write
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| :<math>\frac{\rho - \rho_0}{\rho_0} = \beta \left( T_0 - T \right) </math>
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| where:
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| * <math>\beta</math> is the volumetric expansion coefficient
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| * <math>T</math> is temperature
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| * subscript 0 refers to a reference point within the fluid body
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| Doing this gives the [[Grashof number]], i.e. the Archimedes and Grashof numbers are equivalent but suited to describing situations where there is a material difference in density and heat transfer causes the density difference respectively. The Archimedes number is related to both the [[Richardson number]] and [[Reynolds number]] via
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| <math> \mathrm{Ar} = \mathrm{Ri}\,\mathrm{Re}^2</math>
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| ==See also==
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| *[[Fluid dynamics]]
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| *[[Convective heat transfer]]
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| *[[Galilei number]]
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| *[[Grashof number]]
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| == References ==
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| <references />
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| {{NonDimFluMech}}
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| {{DEFAULTSORT:Archimedes Number}}
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Fluid dynamics]]
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| [[Category:Archimedes|number]]
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| {{Fluiddynamics-stub}}
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They call me Mari. Some time ago I decided i would live in Kansas which can never work. Playing handball is what my in addition to I get pleasure. For years I've been working for a production and planning police. Go to her website to find out more: http://waldob9.blog.com/2014/06/15/reciclaje-funcional-de-la-fibra-de-vidrio/