apph 4200 physics of fluids - columbia...

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APPH 4200 Physics of Fluids 1. Phasors 2. Surface Tension 3. Capillary Waves 4. Rayleigh-Taylor Instability 5. Sound 6. Organ Pipes 7. HW 4 More Fluid Waves (Ch. 7) November 17, 2009 1 ~ ~ C: \) .. CD ~ 1~ ~'t ~ F QJ "v \\ "" cr.. \l \\ i C " ~ tJ j II \1 \l \. 1I V\ ~ ~ ~ c; ... Q ~ t; "" I ~ ~ 0 r. ~ ~ v' ~ ~ r 't () -irJ -;rJ c: Il) :r 1 ':r r- " c- ~ ~ Cl ~ Il 2$ lJ l/ '- ~ c. - VI ct - r" 0 -- ~ ~ /' l i. -\ (' II '- - ~ 't ~ ~ ') J J _....- /" ~~ -- N Y. l ( ~ ./ .. y. ~ If x ,J ~ "- Q ~ l" '\ '- "- \/ 1I J l . ~ '~ \) r- \ ~ \D "- -L ~ ./ . Î ~ \\ ~ \ \: +- i' \ ~ "- t- ~ ;: 'i J \) .. ~ ~(~ :) " (' l ' o. '" l \J ~Q L ,,~ ,. ~'J x ~ . .. () ~ ~ ~ li U ~ "- v- 'V '- c: ~ \) \. ". ~ \. \\ \) -v /' ~ j -J /' '+ ~ ii I '\ J I j I Ii ./ 'i '" i .. IJ ~ ~ '" ~ 0- .. ~ ~ 'l j + -- J -; "" ~fv ~ 0 \ L J 0 () 0 ~ 'i \ ~ "- '- ~ c: .. 'i \ ~ ~~~ "- \. ~ ~ \ " ~\~ ~ ~ f' ~ \f t' - 0 .. '~o (C r: \. ~ () ~o ~o ( '0 'J "" Phasors, Sine, Cosine 2

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Page 1: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

APPH 4200 Physics of Fluids

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Page 2: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 3: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 5: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 6: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 7: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 8: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

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Page 9: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

HW 1: Ch 7, Prob 1

17

HW 2: Ch 7, Prob 2

18

Page 10: APPH 4200 Physics of Fluids - Columbia Universitysites.apam.columbia.edu/courses/apph4200x/Lecture-18_(11-17-09).… · APPH 4200 Physics of Fluids 1.!! Phasors 2.! Surface Tension

HW 3: Ch 7, Prob 4

19

Summary

• Surface tension acts to flatten short ripples on a fluid.

• Surface tension is a restoring force that can stabilize instability.

• Sound obeys Helmholtz Equation, with the speed of sound related to the "(#P/#ρ).

• Organ pipes amplify resonant sound waves!

20