Nonnegative rank (linear algebra): Difference between revisions

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m →‎Formal Definition: WP:CHECKWIKI error fixes using AWB (9494)
 
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{{about|extensional viscosity||Rheology}}
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'''Extensional viscosity ''' (also known as '''elongational viscosity''') is a [[viscosity]] coefficient when applied [[Stress (physics)|stress]] is [[extensional stress]].<ref>Barnes, H.A. "A handbook of elementary rheology", Institute of non-Newtonian Fluid Mechanics, 2000</ref>
:This parameter is often used for characterizing polymer solutions.
''Extensional viscosity'' can be measured using rheometers that apply ''extensional stress''. [[Acoustic rheometer]] is one example of such devices.
 
:<math>\eta_e = \frac{\sigma_n}{\dot{\varepsilon}}\,\!</math>
 
where
 
:<math>\eta_e\,\!</math> is the '''extensional viscosity''' or '''elongational viscosity'''
:<math>\sigma_n\,\!</math> is the '''normal stress''': <math>\sigma_n = \frac{F}{A}\,\!</math>
:<math>\dot{\varepsilon}\,\!</math> is the '''rate of strain''': <math>\dot{\varepsilon} = \frac{1}{L}\frac{dL}{dt}\,\!</math>
 
For a [[Newtonian Fluid]], the elongational viscosity is three times the shear viscosity which can be derived using the [[continuity equation]] for incompressible fluids.
 
:<math>\eta_e = 3\eta\,\!</math>
 
==References==
{{reflist}}
 
==See also==
*[[Rheology]]
*[[Viscosity]]
*[[Trouton's ratio]]
 
{{DEFAULTSORT:Extensional Viscosity}}
[[Category:Fluid dynamics]]
[[Category:Viscosity]]
 
 
{{fluiddynamics-stub}}

Latest revision as of 17:56, 6 January 2015

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