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{{more footnotes|date=February 2012}} | |||
In [[fluid dynamics]] the '''Eötvös number''' ('''Eo''') is a [[dimensionless number]] named after Hungarian physicist [[Loránd Eötvös]] (1848–1919).<ref name="Clift1978"> | |||
{{cite book|last=Clift|first=R.|last2=Grace|first2=J. R.|last3=Weber|first3=M. E.|title=Bubbles Drops and Particles|publisher=Academic Press|location=New York|year=1978|isbn=0-12-176950-X|page=26}} | |||
</ref><ref name="Tryggvason2011"> | |||
{{cite book|last1=Tryggvason|first1=Grétar|last2=Scardovelli|first2=Ruben|last3=Zaleski|first3=Stéphane|title=Direct Numerical Simulations of Gas–Liquid Multiphase Flows|year=2011|publisher=Cambridge University Press|location=Cambridge, UK|isbn=9781139153195|url=http://www.cambridge.org/fr/knowledge/isbn/item6796659|page=43}}</ref> | |||
It is also known in a slightly different form as the '''Bond number''' ('''Bo'''),<ref name="Tryggvason2011" /><ref name="Hager2012"> | |||
{{cite journal|last=Hager|first=Willi H.|title=Wilfrid Noel Bond and the Bond number|journal=Journal of Hydraulic Research|year=2012|volume=50|issue=1|pages=3–9|doi=10.1080/00221686.2011.649839|url=http://www.tandfonline.com/doi/abs/10.1080/00221686.2011.649839}} | |||
</ref><ref name=deGennes2004> | |||
{{cite book|last1=de Gennes|first1=Pierre-Gilles|last2=Brochard-Wyart|first2=Françoise|last3=Quéré|first3=David|title=Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves|year=2004|publisher=Springer|location=New York|isbn=978-0-387-00592-8|url=http://www.springer.com/materials/surfaces+interfaces/book/978-0-387-00592-8|page=119}}</ref> | |||
named after the English physicist Wilfrid Noel Bond (1897–1937).<ref name="Hager2012" /><ref> | |||
{{cite journal|title=Dr. W. N. Bond|journal=Nature|year=1937|volume=140|issue=3547|pages=716-716|doi=10.1038/140716a0|url=http://www.nature.com/nature/journal/v140/n3547/abs/140716a0.html|bibcode = 1937Natur.140Q.716. }}</ref> | |||
The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.{{Citation needed|date=July 2012}} | |||
Together with [[Morton number]] it can be used to characterize the shape of [[Liquid bubble|bubbles]] or [[drop (liquid)|drops]] moving in a surrounding fluid. | |||
Eötvös number may be regarded as proportional to [[buoyancy]] force divided by [[surface tension]] force. | |||
:<math>\mathrm{Eo}=\frac{\Delta\rho \,g \,L^2}{\sigma}</math> | |||
* Eo is the Eötvös number | |||
* <math>\Delta\rho</math>: difference in [[density]] of the two phases, ([[SI]] units: [[kilogram|kg]]/[[meter|m]]<sup>3</sup>) | |||
* ''g'': [[gravitational acceleration]], ([[SI]] units : m/[[second|s]]<sup>2</sup>) | |||
* ''L'': characteristic length, ([[SI]] units : m) | |||
* <math>\sigma</math>: [[surface tension]], ([[SI]] units : [[Newton (unit)|N]]/m) | |||
A different statement of the equation is as follows: | |||
:<math>\mathrm{Bo} = \frac{\rho a L^2}{\gamma}</math> | |||
where | |||
* Bo is the Bond Number | |||
* <math>\rho</math> is the [[density]], or the density difference between fluids. | |||
* ''a'' the acceleration associated with the [[body force]], almost always [[gravity]]. | |||
* ''L'' the 'characteristic length scale', e.g. [[radius]] of a drop or the radius of a [[capillary]] tube. | |||
* <math>\gamma</math> is the surface tension of the interface. | |||
The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects. | |||
The Bond number is the most common comparison of gravity and surface tension effects and it may be derived in a number of ways, such as [[scale analysis (mathematics)|scaling]] the pressure of a drop of liquid on a solid surface. It is usually important, however, to find the right length scale specific to a problem by doing a ground-up [[scale analysis (mathematics)|scale analysis]]. Other dimensionless numbers are related to the Bond number: | |||
:<math>\mathrm{Bo} = \mathrm{Eo} = 2\, \mathrm{Go}^2 = 2\, \mathrm{De}^2\,</math> | |||
Where Eo, Go, and De are respectively the Eötvös, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (which arises in wire coating problems) uses the letter ''R'' to represent length scales while the Deryagin number (which arises in plate film thickness problems) uses ''L''. | |||
==References== | |||
{{Reflist}} | |||
{{NonDimFluMech}} | |||
{{DEFAULTSORT:Eotvos Number}} | |||
[[Category:Dimensionless numbers of fluid mechanics]] | |||
[[Category:Fluid dynamics]] | |||
[[ru:Число Этвёша]] | |||
Revision as of 20:50, 8 November 2013
In fluid dynamics the Eötvös number (Eo) is a dimensionless number named after Hungarian physicist Loránd Eötvös (1848–1919).[1][2] It is also known in a slightly different form as the Bond number (Bo),[2][3][4] named after the English physicist Wilfrid Noel Bond (1897–1937).[3][5] The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
Together with Morton number it can be used to characterize the shape of bubbles or drops moving in a surrounding fluid. Eötvös number may be regarded as proportional to buoyancy force divided by surface tension force.
- Eo is the Eötvös number
- : difference in density of the two phases, (SI units: kg/m3)
- g: gravitational acceleration, (SI units : m/s2)
- L: characteristic length, (SI units : m)
- : surface tension, (SI units : N/m)
A different statement of the equation is as follows:
where
- Bo is the Bond Number
- is the density, or the density difference between fluids.
- a the acceleration associated with the body force, almost always gravity.
- L the 'characteristic length scale', e.g. radius of a drop or the radius of a capillary tube.
- is the surface tension of the interface.
The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.
The Bond number is the most common comparison of gravity and surface tension effects and it may be derived in a number of ways, such as scaling the pressure of a drop of liquid on a solid surface. It is usually important, however, to find the right length scale specific to a problem by doing a ground-up scale analysis. Other dimensionless numbers are related to the Bond number:
Where Eo, Go, and De are respectively the Eötvös, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (which arises in wire coating problems) uses the letter R to represent length scales while the Deryagin number (which arises in plate film thickness problems) uses L.
References
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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
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