ME-509

ME-509 - 0.4 nm Displacement distance 1 pm Molecular...

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8/22/2006 ME509: Fluid Mechanics 1 Fluids Basics •Definition of Fluid : –A fluid is a substance that deforms continuously under the application of a shear (tangential) stress no matter how small the shear stress may be. –Liquids and gases •Liquids and gases are very different –Liquids become less viscous as T increases –Gases become more viscous at T increases Why? 8/22/2006 ME509: Fluid Mechanics 2 Two Approaches for Modeling Fluids • Continuum models – works when point quantities can be large enough to contain many molecules but still small compared to the scale of the flow • Molecular Models – must be used when these conditions are not met
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8/22/2006 ME509: Fluid Mechanics 3 The Smallest Length Scale of a Continuum (Deen, Analysis of Transport Phenomena, 1998) Gases (STP) Molecular diameter 0.3 nm Number density (m -3 ) 3 E25 Intermolecular spacing 3 nm Displacement distance 100 nm Molecular Velocity 500 m/s Liquids Molecular diameter 0.3 nm Number density (m -3 ) 2 E28 Intermolecular spacing
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Unformatted text preview: 0.4 nm Displacement distance 1 pm Molecular Velocity 10 3 m/s 8/22/2006 ME509: Fluid Mechanics 4 The Smallest Length Scale of a Continuum (Deen, Analysis of Transport Phenomena, 1998) Average over sufficient number of molecules Point quantities, , u , T Random process theory N ~ 10 4 molecules L ~ 70 nm (gases at STP) L ~ 8 nm (liquids) Point Value Macroscopic Value Averaging Volume ~ L 3 2 / 1 N x 8/22/2006 ME509: Fluid Mechanics 5 The Smallest Length Scale of a Continuum (Deen, Analysis of Transport Phenomena, 1998) Length scale of molecular interactions (transport properties, , , D ) Gases: mean free path ~ 100 nm Liquids: molecular diameter ~ 0.3 nm Average over ~ 10 3 interaction length scales L ~ 1 m (gases) L ~ 3 nm (liquids) Taking the max of these two types of quantities L ~ 1 m (gases) L ~ 10 nm (liquids) 8/22/2006 ME509: Fluid Mechanics 6 Gad-el-Hak, 1999...
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ME-509 - 0.4 nm Displacement distance 1 pm Molecular...

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