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Lecture-6 - APPH 4200 Physics of Fluids Fluid Equations of...

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APPH 4200 Physics of Fluids Fluid Equations of Motion (Ch. 4) September 22, 2011 1. Conservation of Mass 2. Navier-Stokes Equation (Force-Momentum) 3. Mechanical and Thermal Energy 4. Entropy 5. Some examples 1
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Equations of Fluid Dynamics (Conservation Laws) 2
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Newton’s Law 3
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Continuity Mass 4
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Momentum 5
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Momentum x-direction ) ~ ~ "' ~ ~ ) .. ~ ~ ~ q~' ~ /" ~ i: y '- r- v Vi ~\l ~ '- '-Ji l.u ~ ~ ~ '4 \J '\ .. /I ~ - lt ~~ hJ l~ 1 Q I. ~ ~ \ ') J V) - r; \ i ('b ¡: J -= - o I:: L r' l lL l ~ ~ .. rN l - ---\L ~2J " ~\ .l ~ " "' ~v 33 (\ + + l + )- rG l \! '. ~ I. "- ~ "J '1. ~ ~ G- \"' ~ .J V I l ~.) "- ~ "- r\ rl )- ~ I~ ~ ~ -: )- l" '" X .. I~ ~ ~ l~ + -+ '- + 4- ri ~ "1 l:r \ ,¡ ). -: I. ~ ~cb )/ ~ ~ ~ ~ ~ ~ ~ ~ Vl II \'t I~ 0- ,~\(~ 3 ¡ IJ \ -j ) i (: C: . ~ \J I) ii ~ .J ~ .. C ~ 0 1- . ~ ¡~ :: r= l. V It. L -- ~ .~ - ,. Q ","X .. (~ l "X 6
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Osborn Reynolds (Reynolds Transport Theory) Q. ~ J .. '0 ~ j J \i ~ ~ ~!\ IV ~ ~ 1 r\\, t ~ ~.\ ~ l. Ii l' ~ .) ~ ') ~ ~ I\\.j .. ~ '- )- f ~ ~)( l~ ~~3 ~..) ~lL t~ i r " i~ \S t; '- ~ '- ~ /" l\~ i I~ 1- l~ Q. ~ J ~ Çi c= lt I J ~ \~ ~ ~ ~ ~1 o lJ l~ . ~ Qn + ~\ "i (. Q I) /" W o- ~ ~ + ~~ \LJ ~ - \J \ l~ 1; ~ i I~ -r /" I": \ ~ ~ r- ~ L J ~ ~~ ~~ tI \ l~ l~ ~ ~ . /" ~ ~ L ': Q + 1- r ~;: l~ 4- b\'- C" l' l &. 1 ~ ~ '\ ~~ t:~ \1 l~ ~ ~ ~ ',- ~ ~ .J ~ 'i ÇJ\.8 l i l~ \ .. Ci a ~ ~ ~ '- ,,1 ~.~ 1842-1912 7
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Models for Stress 8
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Navier & Stokes George Stokes (1819-1903) Viscous flow, Stokes’ Law Claude-Lewis Henri Navier (1785-1836) Elasticity 9
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Pont des Invalides 10
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Stokes Flow 11
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Tay Bridge Disaster (1879) 12
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Stokesian Fluid 13
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Navier-Stokes Equation 14
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Navier-Stokes & Euler 15
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