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Lecture-24_(12-10-09)

Lecture-24_(12-10-09) - APPH 4200 Physics of Fluids Review...

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APPH 4200 Physics of Fluids Review December 10, 2009 23 Lectures > 700 pages of text 1 Lecture 3 Velocity gradient tensor, strain, rotation 2
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Deformation and Flow: Translation, Stretching, Pinching, and Rotating 3 Simple Comments about Velocity Gradient Tensor 4
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Stretching along one Axis 5 Rotation 6
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Bending, Distorting, Shearing 7 Example Shearing 8
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Lecture 4 Navier-Stokes Equation 9 Continuity Mass 10
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Newton’s Law 11 Momentum 12
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Models for Stress 13 Stokesian Fluid 14
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Navier-Stokes Equation 15 Navier-Stokes & Euler 16
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Lecture 5 “Equations of Fluid Dynamics” 17 Equations of Fluid Dynamics (Conservation Laws) 18
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Navier-Stokes & Euler 19 Mechanical Energy Density for a Stokes Fluid 20
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Summary of Fluid Dynamical Equations 21 Lecture 6 Bernoulli’s principle Co-rotating frame 22
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Incompressible Navier-Stokes in Co-Rotating Frame I t: ~ "'~ b l t: I~ "" \J l~ ¡ :i 'o o T .. ~ I ~ ~ \l 'Q ~ .. rv ~ i ~ ~(~ b(~ '- l- L ( "" i' \~ (" . " ~\~ ,:4 l : ~ il ~ i + ( (ï l~ ( l Ii c; I~ I '~(~ ~ ~ . . r \: ;. \- \) c: ~ d: \ -J 0 li 25 Lecture 7, 8 Vorticity Kelvin’s Theorem 26
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The Importance of Viscosity 29 .. ~ i 0 y r- , ¡:.. 0 1: Q ~ F .. ~ II Q * Ç) ~ 'i V\ - .. ~ lL )l ~ :, J :i ~ -; ,.. tJ .. ~ \J L. ~ .~ \D \I 'f i - "" " ~ J ~ tl ~ J l , . " \1 c\ ~ ~ ~ ~ . ~ l. ~ k r- j ,'- 0 - ) ~ II r l( '- j w \ i rv ,. ~ , 1 1 iv ~ ~ j, J ~ ~ ,~ t' '- r. l\ 0 - ~ \l ~ 0' -- -i ~ I~ ~ ~ I:. ~ .. ~ ~ ~ - .. ~ II to .. a ~ \) '- '; (J \I fi L- t ~ v C J i ) \I S - ~ Oö " c () \p '- "- , -- "- --...~ ./ ) ) ). " 'i ai "0 l- 0 ,: ~ - t Ll (- ~ i ~ ~, ~ I\ :) \. ~ \) .. ~ lo lL Q U V\ - Ql i. .- 0 ~ ~ -( ~ C d ? ~ ~ ~ 0 () Hr ~ (' '" .. ~ .. Q, r- -( , \I i l t. VI ~ /3 ~ 1- 3 3 t 1 ~ ri CJ ~ \ , "' Q v r: ~ (j il ~ \I ~ \J - ~ :J - ~ ~~ \- \f 0 l~ ~ Il 'X ~ oJ ~ .- 0 ~ Cl ~ ~ r- ev -- -. I- g ~ )- \. -' .. oJ \t CJ - -' \... ~ II C: 0 ~ .s Simple Fluid Rotation 30
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