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Lecture-13_(10-19-10)

Lecture-13_(10-19-10) - APPH 4200 Physics of Fluids Laminar...

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APPH 4200 Physics of Fluids Laminar Flow (Ch. 9) October 19, 2010 1. Dimensional analysis (again) 2. Laminar flow (when viscosity exceeds advection) 3. Examples: Poiseuille’s steady flow through a pipe 1 J~ (" ~ ~ ~ ~ XL~ ~ ~ i~ -t ~ II l~ .l -l~ iJ " u ~ I~ i ~ f~ ~.-- ~ ~ .~ ll" IJ \ l i ~ -- 1I /J F . ~ ~ \) I~ ~ Th. i ~ ~ u ~-. .. l J ~ 1'- \ , A ~ t II v v- L J l:J .. V ~ ~ " '- V1 0 CL "- .,L V) ~ l~ ib + v v ~ ~ t .. A l:j b\ ;. l ~ ~ le- t" C1 Cb i l t( .r :: T UJ -- CJ Q.\ ~ -1 LL v Jl "' VJ CO C' ~ i ~ '~ . . -i ii .. ~ '- t ~ V' io ~ "- Ii ~ ~ \/ ~ "- t ~ l ~ V' '\ ~ \ Ll. l ~ J VI t \:' ~ a .. ( ~ - c. ~ D 0 LL v ~ Dimensional Variables 2
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\. "- t~ I:J f' " "v '- Q. "- \~ ~ ~ ~ ~ ~ ~. ~~ N ~ ~\~ J ~ h " 'i -)~ l~ -\ :: ~ -1æ ~ ~ , Q. ~ "- ~ " , J Q. + l~ "- ~ ~ '" ~ '- ~ \ i. -L L~ " Q. ~ , ti .: ~ c' ~ S j -A 'l II \I \. \L I ~ I) F "- 2- " \A ~ "- \~ 1 ri .. "t \I ~ ,,~ i :: ~ "- 1m ::. i ~ ( G. çi "- i.. J I~ lb .J Q Ç) t l/ c¿ t "- lL '- .. " . ~ i :: I~ ¡ 1:: :r u " i- -i l. l'\ t v N - '- . " ~ sl l~ Q. )' '\ ~ '0 ~ l:: \ \- ~~ L a v rc n ~ VI Q '- .. )-- t \l ~ 1\ I l:: ).. 1- ß \l .. .: CQ C) ") Q ~ ~ i. ~ I~ i ~ ~ lW ~ J \/ ~ '- v lQ ') 'C ~ '- !. \L ~ ~ ~ H Q. Dimensionless Equations 3 Incompressible NS Steady Laminar Flow! 4
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Laminar Flow (Ch. 9) Two simple examples: Couette Flow (moving top plate) Poiseuille Flow (pressure-driven) ! Steady with viscosity 5 Maurice Couette 6
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Couette Flow 7 Jean Louis Marie Poiseuille (1799-1869) In 1838 he experimentally derived and in 1840 and 1846 formulated and published
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