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| The '''Bagnold number''' ('''Ba''') is the ratio of grain collision stresses to viscous fluid [[Stress (mechanics)|stresses]] in a [[granular material|granular]] flow with interstitial [[Newtonian fluid]], first identified by [[Ralph Alger Bagnold]].<ref>{{cite journal |last1=Bagnold |first1=R. A. |year=1954 |title=Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear |journal= Proc. R. Soc. Lond. A |volume=225 |issue=1160 |pages=49–63 |doi=10.1098/rspa.1954.0186 |url=http://dx.doi.org/10.1098/rspa.1954.0186 }}</ref> | | The individual who wrote the article is called Jayson Hirano and he completely digs that title. Mississippi is the only place I've been residing in but I will have to move in a year or two. [http://cartoonkorea.com/ce002/1093612 tarot card readings] What me and my family love is to climb but I'm thinking on starting something new. Office supervising is what she does for a living.<br><br>my blog: online [http://isaworld.pe.kr/?document_srl=392088 best psychic] chat [[http://chorokdeul.co.kr/index.php?document_srl=324263&mid=customer21 please click the next post]] |
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| The Bagnold number is defined by
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| : <math>\mathrm{Ba}=\frac{\rho d^2 \lambda^{1/2} \gamma}{\mu}</math>,<ref>{{cite journal |last1=Hunt |first1=M. L. |last2=Zenit |first2=R. |last3=Campbell |first3=C. S. |last4=Brennen |first4=C.E. |year=2002 |title=Revisiting the 1954 suspension experiments of R. A. Bagnold |journal=Journal of Fluid Mechanics |volume=452 |pages=1–24 |publisher=Cambridge University Press |doi=10.1017/S0022112001006577 |url=http://dx.doi.org/10.1017/S0022112001006577 }}</ref>
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| where <math>\rho</math> is the particle [[density]], <math>d</math> is the grain diameter, <math>\dot{\gamma}</math> is the [[shear rate]] and <math>\mu</math> is the [[dynamic viscosity]] of the interstitial fluid. The parameter <math>\lambda</math> is known as the linear concentration, and is given by
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| : <math>\lambda=\frac{1}{\left(\phi_0 / \phi\right)^{\frac{1}{3}} - 1}</math>,
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| where <math>\phi</math> is the solids fraction and <math>\phi_0</math> is the maximum possible concentration (see [[random close pack]]ing).
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| In flows with small Bagnold numbers (Ba < 40), viscous fluid stresses dominate grain collision stresses, and the flow is said to be in the 'macro-viscous' regime. Grain collision stresses dominate at large Bagnold number (Ba > 450), which is known as the 'grain-inertia' regime. A transitional regime falls between these two values.
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| ==See also==
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| * [[Bingham plastic]]
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| ==References==
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| <references/>
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| ==External links==
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| *[http://microgravity.grc.nasa.gov/fcarchive/fluids/papers/Hunt/Granular_Material_Flows.htm Granular Material Flows at N.A.S.A]
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| {{NonDimFluMech}}
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| [[Category:Granular materials]]
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| [[Category:Dimensionless numbers]]
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Latest revision as of 19:26, 25 November 2014
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