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| {{for|the measure of the [[quantum entanglement]] of a [[density matrix]]|Schmidt decomposition}}
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| '''Schmidt number''' ('''Sc''') is a [[dimensionless number]] defined as the [[ratio]] of [[momentum diffusion|momentum diffusivity]] ([[viscosity]]) and [[mass diffusivity]], and is used to characterize [[fluid]] flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after the German engineer Ernst Heinrich Wilhelm Schmidt (1892-1975). | |
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| Schmidt number is the ratio of the shear component for diffusivity ''viscosity/density'' to the [[Viscosity#Kinematic viscosity|diffusivity]] for mass transfer ''D''. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer.
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| It is defined<ref>{{Citation
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| | last1 = Incropera | first1 = Frank P.
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| | last2 = DeWitt | first2 = David P.
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| | title = Fundamentals of Heat and Mass Transfer
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| | edition = 3rd
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| | publisher = [[John Wiley & Sons]]
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| | year = 1990
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| | pages = 345
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| | isbn = 0-471-51729-1 }} Eq. 6.71.</ref> as:
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| :<math>\mathrm{Sc} = \frac{\nu}{D} = \frac {\mu} {\rho D} = \frac{ \mbox{viscous diffusion rate} }{ \mbox{molecular (mass) diffusion rate} }</math>
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| where:
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| * <math>\nu</math> is the [[viscosity#Kinematic_viscosity|kinematic viscosity]] or (<math>{\mu}</math>/<math>{\rho}\,</math>) in units of (m<sup>2</sup>/s)
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| * <math>D</math> is the [[mass diffusivity]] (m<sup>2</sup>/s).
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| * <math>{\mu}</math> is the [[dynamic viscosity]] of the [[fluid]] (Pa·s or N·s/m² or kg/m·s)
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| * <math>\rho</math> is the [[density]] of the fluid (kg/m³).
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| The heat transfer analog of the Schmidt number is the [[Prandtl number]].
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| ==Turbulent Schmidt Number==
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| The turbulent Schmidt number is commonly used in turbulence research and is defined as:<ref>{{cite journal|last=Brethouwer|first=G.|title=The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulation|journal=J. Fluid Mech.|year=2005|volume=542|pages=305–342}}</ref>
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| <math>\mathrm{Sc}_\mathrm{t} = \frac{\nu_\mathrm{t}}{K} </math>
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| where:
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| * <math>\nu_\mathrm{t}</math> is the [[Turbulence_modeling#Eddy_viscosity|eddy viscosity]] in units of (m<sup>2</sup>/s)
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| * <math>K</math> is the [[Eddy diffusion|eddy diffusivity]] (m<sup>2</sup>/s).
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| The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar). It is related to the [[turbulent Prandtl number]] which is concerned with turbulent heat transfer rather than turbulent mass transfer.
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| ==Stirling engines==
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| For [[Stirling engine]]s, the Schmidt number represents dimensionless [[specific power]]{{disambiguation needed|date=December 2012}}.
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| Gustav Schmidt of the German Polytechnic Institute of Prague published an analysis in 1871 for the now-famous [[Closed-form expression|closed-form]] solution for an idealized isothermal Stirling engine model.<ref>[http://www.ent.ohiou.edu/~urieli/stirling/isothermal/Schmidt.html Schmidt Analysis (updated 12/05/07)<!-- Bot generated title -->]</ref><ref>http://mac6.ma.psu.edu/stirling/simulations/isothermal/schmidt.html</ref>
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| :<math> \mathrm{Sc} = \frac{\sum {\left | {Q} \right |}}{\bar p V_{sw}}</math>
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| where,
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| * <math>\mathrm{Sc}</math> is the Schmidt number
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| * <math>Q</math> is the heat transferred into the working fluid
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| * <math>\bar p</math> is the mean pressure of the working fluid
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| * <math>V_{sw}</math> is the volume swept by the piston.
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| == Notes ==
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| <references/>
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| {{NonDimFluMech}}
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| <!-- Categories -->
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Dimensionless numbers of thermodynamics]]
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| [[Category:Fluid dynamics]]
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