Course Hero

Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

12 Pages

Lecture-14_(10-21-10)

Course: APPH 4200, Spring 2010
School: Columbia
Rating:
 
 
 
 
 

Word Count: 1730

Document Preview

4200 Physics APPH of Fluids Stokes Flow (Ch. 9) October 21, 2010 1.! ! Viscous Decay of a Line Vortex 2.! Vortex sheet 3.! Stokes Solution for Viscous Flow around a Sphere 1 ~ ~ ~.. .. 'f - -i ~ -: ~ ~ y. ~~ " Q ~.. ( .. -. l \A 0 :l .. t. .~ ci 1:1 J c: ~ ~~ ") .i (! .. ~ .. ~ 'Q ~ y. ~. ~ I 1\ Viscous Decay of Line Vortex r" ~ x .. 1 '\ '...

Register Now
Search

Unformatted Document Excerpt

Coursehero >> New York >> Columbia >> APPH 4200

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
4200 Physics APPH of Fluids Stokes Flow (Ch. 9) October 21, 2010 1.! ! Viscous Decay of a Line Vortex 2.! Vortex sheet 3.! Stokes Solution for Viscous Flow around a Sphere 1 ~ ~ ~.. .. 'f - -i ~ -: ~ ~ y. ~~ " Q ~.. ( .. -. l \A 0 :l .. t. .~ ci 1:1 J c: ~ ~~ ") .i (! .. ~ .. ~ 'Q ~ y. ~. ~ I 1\ Viscous Decay of Line Vortex r" ~ x .. 1 '\ ' \) 0 ~t\ ~ F ," ~ "0 ~ .. i \! .. ~ l.. ~ J. u t ~ ~ ~ ~ .. VI '\ " tI Q .. i ~r . '- '- v .\ . .. " ~ ,f ( L t ct "" l "" ~ ~ u 'U ': .. ~ l. ~ '- VI ~ ~ 'i Q,\ t Q \ ti t' ~\" l! .. '- i- ~ i ~\~ C1 C\ ., ~ (\ l \. ct ~ )l ef ": ( l; C' ~ 0 rl ": ci .,~ u ~l~ l~ "- .. -l ( N (\ .:40\ ( J ~ IcJc. ~~ ~(1. ~ . ~ o'\~ "i ~ "- tl~ ii ri fl l' \~ -,~ /" i (. ~ ~ f ~ l'j '- ~ ct ~ iI "" .. oJ ~ ~\ c. .. ~, + ow ~4 i~". ~ ~ . rl t . .. l:i tI ~ " ~ ~ 1 . r" .. ~ -l ~ ~ \ u ~ '3 ~ . ~ '" .. .. t " .. \~ ~ ~ , , f! ~ .. ~ ~ 1 .. 'u a ~ ~ \J t - f ~ 0. (" Q - "" t \~ .1' '" i-l tu ~ /' )~ ~ Vl 3 :i ... .i ~ "" F -. i- ~ II J \. : .. ,- c:i ~ a ~~ \b :i ~ 'I ) .. '0 \1 0 ~ () ~ U: 1 ct tJ 2 ~ l~ ~ ~ V\ L - -i ~ lI \) .. f, ) Similarity Solution f ~ \A ~ ~~ ~~ i "~ .. -0 V\ 'b l' ~ i ') ~ r: I( "".. J \J '1 '" ~ ' , va \I "l - i. , \I Gi ') L. r w -; ~ u: .. t: 'c i .. .. ui F '" i .. ~ 4 .. ~l '" \t 'C ~ () \A l ~t -~ ~ i) ~ ~ \ L t. N "' it .) .. tl ~ ~ ~ \J l \\ l 1 -l u. . l .. .~ ( "... ( ~ lt ~ - J "" \e \J ..' t' .. l 'l .J Q 0 ~ ~ ,. \ ~ . Ul i: - .l, 0 ~ Q. a l. L d t E 1: ~ ~ 0 i; ) .. ~ \I ~ .. l - .. .( .. (j ~ ~ l, ~ ~l G I" , 0 .~ ~ F J .. ~ l/ ! l.l I - Vl ~\~ t U 1:\ t -:\ ~ 1, l=\ t' ~ ,. :s) . U- ~ ("l" 0 ~\1J ~'(' .. u. \I c.i ~ N ~ '",. .. i ,. :t ~ ~I~~ )o Co J f:1 ( ~ (" '-" \i ?- I, ~i ~ .. \i .. ~ '\ ). .. I"" 'l Q ~ ~ ~ - '- ~ Ii 1 .. h. J f- 1 4 i \:. \ .. \L .. l .. '0 v li \d ~ c: .. '.. f' t" ,, t, \\ ~ i n" ~I ( -r c. l .. r- '- ~\~ II ~ .. .. \U I . .. ~ ~ 'i .. t: \I l~ t V\ :rliJ ~I"t t1 t\ t . C" t :: \A -, ~ I r;(~ ~ ,. t' "' ~\lr u- .. .. .. ": ( ~\ iJ ~ fl N ~ c" l' .1 ~r~ r' II .. ~ c.1 ~ ~ l.. (~ .t '" . ri Ii " -. -:tl \l N .. c.1 J ll t: "" ,- ~ ~ 1 ~ ~ oJ ;:. -- \J ~ '" 0. ~ \1 V .. .. - ~ oJ ~ ~ ~ t- Similarity Solution '" ~~ ~~ L \A # q, ~ i. ~ .. Q ii .. "" .i -t IJ r" ". ~ l' 4i () l t! ~ '- ~ u. Y ~ i "" 'lt ~ s ., t- l J t .. ~ " ". ~ F- \L r '- '\L ~ .t ~ 'd .. i: J ~ ~Q .. ~ '" ~ , II 1 ~( ~ ~ ~ t-'" ~ '- ~ U t ow \l \l ~ c; a- ~ rJ , ~ ~ - - ~ /' C\ ~ ~ - r "t i t .. u 4 tt VI .. \e ~ r- ~ Q \f ~ ~ iJ Q "" 1c \J ~ V\ .. .. ) oJ Ie J .. ~ (. ~ J J ~ .. - , ) 4 .. ~ ~ \l. \L - 0 ( - "" 3 ~ \ \\ I' (; ,~ '9 'u. \l \1 - ~ v. Q) i: 1 ti '" \) : ~ ~ .. ~-- t: \L J: '" It ,, ~ .. \L l. - ~ .. \ 'l F- + t. - \ \L .." .. 11 , h -- .. '-\~ (i C" 4 (t i ~ 0 t' \- v - .. ~ Q - \L \L. ~ VI .. '= Vorticity Diffusion -- ~ .. ro~ ). ~ J~ 'r.\ ~ ii /" ~ l ~' ~if .. \ ', :s . .. ~ " .. .. "" "" o ~ ~.o .. ~ ~ .. ~ ~~ ~ ,. t" ~ I (\, -l )i ,. ~ .. .p rl ~ t' ,. l d r-\ ~ i1 i X ~ ~ , ~ ~ 0\ ~ "" t.\~ rl\~ i -l ~ " :i II C) .. . t" .. (- 'Q ~ ': t ~ 9 Ui .. Cl ~ '" ~ 3 :r .. -i n \& \4 J ct 't l . ~ G- o~ .. " ~ .. ~ \A tL ~ \. Q .. A t' 5 ~ f' . ~ l. ~ i: J ~ J' - ~ ~ l: '; i: V What is a Vortex Sheet? ~ .. ~ ~ ~ , :: .. "' 'f .. v .. ,. 'Y \6 5 l , -. ~ 'l ~ oJ ".. ~ ~ .. ~ .. .J ~ t ~ L. 1 1f .. tQ l9 ) -~- IE :: lt ~ cJ ~ ~~ l - ':- .. 0# t: A ~ - '" v~~ ie ~ . I~ ''t ~ ~ ~ i\ l": l~ II r. ~ I. ~ 4 ~ i . tI ~ .- (J :rll 1 ,~ ~ ~ ~ i -l :: tl ~ ~ II ~~ ~ '- - ~.. :r ,0 ~' ,-, i. '-~ ': .. u (~ .3 F .- ')\t" ~ 1- r" c1 Il ;: :s \ l' C" C\ .. VI ~ ll I': vi I ~ .. ) l 4C ~ 'Q i: '0 .. ~ \. ~ .. .. i .. .. ( - ~ f, tf i: .i ll ~ i. f. Ca ~ ,, ~ ). ~ u. It ~ i..' '- .. .. f\ i. \; Q " ~ ,. ~ l ~ ~ ~ '" .. ~ "" 0 IU ti i- .) l" . ~ c: \i ~ P- ~ -- ... - "1 i. 'l .. . ~ ~ ~ "" ~ 0 ~ - ~ I ~ ~ .. lt .) ~ 'V \I .. .. 'I i. .. "- li , /' ~ ~ i. '- i f '- ~ I .: ': ~ ~ .. "" h ~~ Q ~ i. '- -. ~ "\ \1 ~ "1 4l 6 ~ .. ~ .. ~ ~ 1 ': "" "" ~ l1 tl - Q w ,.. \l. i: V ') ~ c: ~ ,: ~ t, F: III .. ~~ ~ L- ).. "\ ~ .)~ "" ~ cJ ')1 ), t" M t" )li n 'l ': It) /' v ~' l. ,-, .. "' 11 ': "1:J .. U- ~(~ -l (I (i F( 'i t" C' \L .. " .. -lt II ~ U- .. ~ f:(~ -I~ \ cC \ ).. t" l\ \L .. II :ri il- ~ o l' ~\ l' , ~ ~ V\ ). '.. F: lL I (" \L - ti .. , () 'l , -\t ~ \L ~ h (0 ~ 0 ~ ~ (l ~"" ~ '" : ~ ~ C' \ U :: l. N d "I I ~ 'J \ ). t. " II .. ~ Fe , .. 1 "' ) "' ~ ~l ~~ i: ... ~~ ~ CJ F \ f .) ~ -. II '- L ~~ t: -~ N It ~i~ II " - )\J - 1- ~ .0 \- ~ .. ~ N\~ II 1 .. It \1 ~. ~ .f i :: ,~ '" ~ \l ~ ~ .. . t. ~ \L ~ ~ \~ i: .. .. l ~ tv \t ~ :c ~ . '" ). ,c \ ).. \L t" l\ ~ "" 1I C" ~ "J t" cv i)- ~ .. . x2 2 Out[3]= D x Erf , x In[3]:= 5 4 3 2 1 All ; "Erf x ", PlotRange x, 0, 5 , PlotLabel Plot Erf x , In[2]:= Vortex Sheet Diffusion 7 Error Function 1 Erf x 0.8 0.6 0.4 0.2 8 (g .. fl\ " I~ )( 4 I l(I ~ It: ~ 0 H \) ~~ (t Ie: . l~ ~ ~~ LI ~ - .. .. l ~ ~ .. .1 "" .. ~ \J l. .J ~ 10 (l ). 1 ~ ! Analogous to Magnetic Diffusion ~ .. ) .. ~ ") ~ Q \) ~ .. "" tJ ~ v I'" ~ \U Il \0 lh \! If , \! (" n Q1\ .u II UJ )( ~ i- -i 0 ~ ld 't ib \. )( l~ i "l~ If rh 'A "" , c: ~ (I ~ \(~ .. I " b \ \J o f\ 'c ~ la ( Il ~ t J ". .. lL .. ~ 0 V .. va J \I : 't ~ C ~ .. ~ ).. ,. ~ .. " l- ~ l r ( ( ~\~ (h 0 \1 ~ ~ \) 1 'Q ~ ~ ~ .. 1 ~ ~ ) .. '" 'l 1 ~ .. Q 'V " It ~ \) ~ ~ ~ 'V 1 .. ~ .. ": .. u. '\. a ~ " "' ~ V' v J . 9 Stokes Flow 10 ~ ~ ~ I\ ~ ~ ~ c: l 3 ~ ". l: ll ~~ l\ (:r tV l) ., ~ ~; ~ t: . ~ l~ II , t) \) ~ (l ... J .. "" ~ \: ~ ). tL .. , ~ rl ~ 1 ~~ r'" ~ ~ .. .3 . ~ c: l. l- l' . .. .. - ~ 'C' i :i .j t .I '0 't 'C 1: ~ ~~ '- .. . . 3: 0. ~ (l JI lu '\ ~ \L ~ (~ ~ i~ ~ t: ' ~ ~ '- l ). 'l "' .. 1 ~ '\ ~ ;( ~ t" ?0 .~ t: ~ 1 V) "0 i '\ I J ~ \) "\ c: 1 ~ '" ~ J~ l .. o t "" b~ (I t' II I (L i~ /~ .. tJ l\ ~ .. ~ .. " '" ~ ~ ~ o ~~~ \) ~ 1I ~ () ~ ) lt ~ .. 4 ~ 1 .. lL ~ .. 1: '& b V\ I~ Q. ~ (I j l -( f. ~ .. (~ J tv~ ~ , ~ tL .. J ~ ,i ~ ~ ~" tL .. ~ ~ ~ r ~ r ~ ') .. ~ "' ~ o 'j .\ ~ ,~ tV' VI L/ -. Q (: "i L l ": .. Vl ~ \J i -. tL 1 \) ~ ~ i: t~ ~ v Stokes Solution for Viscous Flow Around a Sphere (1851) . .. \) ,. ). ! ) ~ !~~ ~~i b f' I': i~ ~i ) ~ ~ ~ \~ \l "'" tl. (( ~ ~ ~ VI ~ i,. i .. l-- ~ txJ i:" u. il ~., t b ~~lI (O ~ - ~ -\ri ~ ': ~~ ~ \A () Q .. 1 i"" ~ '3 j tV 't ~ ~ 1; ..,. ~ li q, II " , ~3 :i l.. ~..~ ~ ~ '- :) ~ \"~ ~ ~( :j t ~ I~ t II ~ ~ I) ( 1 ~~ I\: .l .. ~ .. 0 , ~ ti \A , I -. ~~ ~ I~ ~ r: '. ~ t \A '* :t .. ~ 4: ~ ~ Vl ~ ot l. '" ~ ".. .. ).. " .. J \J c: '.0 \u ~ .: -i 'l ~ .. Steady, Creeping, Flow Around an Object 11 ' . ~~ \I ~ .. " ~" i ~l ~~ i: VI '- t J _. Il ~ "t ~~ :r \o.. \l -~ F~ t ~ ~ ,. '1\ " ~ '- x ~ \ ~ ~ ~ I ~ '4l /" J~ 3 l~ " \.) ~ ~t" (\ \) I~ II i~ ) ~ h I ': l"tJ )! () ~ ). .. \l - ., l - '" t "' ~ .. ~ ~ "3 ~ ~ v .. ~ ~~ l. \. \) ~ '" t( I~ ':= /' ,. J VI ~ .. to t ;; .. 'l! to ( r ~ ~b ~i lJ , 1: ~ V\ ~ .. 12 Stokes Flow (1-3) 13 Stokes Flow (4-5) 14 ~ ~ 1 ~ \I .i r; :) "3 .) ~ Vl ~ '0 ~ :J ~ 'i ~ Stokes Solution (some algebra...) r~' i-\ b ~" ~ -I ~ ~ N\~ -\~~ .. ., " 'C ~\J --~ .. )( ~ l c; L -. -l .t l U l:~ ~'\ ~ ~ ~ \ l\ i r- _\ l" ~ t'\ ~ -I! ~ cJ\~ ~ , ~~ ~~ ~ ri\~ ~~ -; \ i ,~"~ l.. rJ l- ( 1 ~ ~\~ b ci ,~ -l ! "'.. ~ 1 \ .l ~~ + T .. -i ~ \ I\~ l \ II -\( ~ l- ci ") '\ ~ .. Q) \I ~ ? ~ )( -1 /' Ii ~\~ Lr ~ '-lt rl\~ ~ ~ -\ ~ \t. li l~ ~ ~ rr- 1 ~ ~ \\ t V. ~ tl\~ C) t\ (" \ \\ l I.. \; 1\ ~ ,. ~ ~ r N t" ~ -i l "" ~ "" .. , l i ~ " ~ ~\~ \I .. ~ ~ rl\~ ~ l -i "- ~ ~ 'i ~ /'l ~ , '" -. \b .. i _. i~ ,. --, ~ti . -' ~ \\ ~ f\ ~ :) -i cl\~ i -l~ ~ r(\~ iI \I '\ ~iJ VI T .. , \~ N .. L II I.. l3 \: U\ ~ ~ Vi ~ ~ ~ X ~ \\ r ~ "" \ -H ~~ ~ cL 15 Stokes Flow (6-7) 16 ~ .. \l ~ ll t. "" \I ~ -l ') r: ~ () b ~ t' \\ ':t ob \,i rI . (l LJ T ~rt .: cJ \ ~ -\ V\ ~ '- cJl~ r) ~ r' Stokes Solution (some algebra...) rJ C) q ~ ". ~.. .. -) I\ t'l~\ ( r C) u ~ 'h t' '" ~ ':t \ :: ~ + (' \ tI" ~ '- tl \,. .. ~ I .. NI~ .. , l' )..~ - -l l" i .. '" rJ ,. "'I~ I .. Oo~ 1 /' ~ \ri ,-\ ~ " I ~ ~ (~ 3" \ ., \ C l- L ~ Ii o '\ I .. (~ .. + "\ l" ~\ '\ - .. .. .. \. , ~ \,J ~ ,, ~ ~ ~ iJ ~i t. -,'" ~ ;. '" "" .. r -i J W(~ '" .. l/\ t M'\ t\ Q) I ~ l , ~ " tv ~ ..1,J II -. ~ . . ~ '- .. l: '" tI "3 "" " tlN .. ~ l- C' 't ~ ., ~; i- r" IJ 1\ ~ ( ~ ~~ ff \ ~~ ,. ,. " ~.. -i~ l\ r- j- , ~ ~ .. .. Q ~ 17 Stokes Flow (8-9) 18 Stokes Law Stokes, G. G. "On the Effect of the Internal Friction of Fluids on the Motion of Pendulums." Cambridge Philos. Trans. 9, 8-106, 1851. CGS unit for is poise (Pl) and for / is stokes (St) 19 Problem 9.1 20 # "" .. ~ ~ o ~ l:i 'b l' .. I (l" ~ Ii .. ~ l:s C1': '~ - i ~ ;it l"~ rc ~ "l 4) ~ .. ~ .. '" \( i. ,. . ~ \). t\N I ,) l. .. '\ 1. 'J Q 1; 'l , ti " ~\). '0 '" ~ t ., t. - c l '" \ ~ \I f~ ~\l II ~tj ~ J.1.c i ~~t ~). ~ L ~.. \ ,. ~ ~ .. Ii -c \J /' GJ ~ '- ~ tf r\.. r n fi i I' II -i ~)-\ .. ~ i-' .. ~\~ *~~ ~ I Irl ~ , 6'\). '- '" ~ \\ va ~ " . , . ~ i: ~ l/ 3 ~ t: Vi ~~ ii (I ~ --\,i ~ i, II t.. 1,J II .. _oJ .; ($\ ). ~ \)", '- t , C'" J. ii ~ ~ \ ~\rIC1 t1 II .. . ~ i. .\ )~ Q .s .. ~"' ~ ,. . . .. \A ~ 1 '4 C) ~.. ~ \\ i. ~ VI It h :: Q t~ -: tJ .), '- li ~ ~ .i () .. ) i , t o i tl t('C \I ~ v~ 9 F .. L ~ tI ,.. l 1 Y Q Viscous decay of a line vortex Stream lines and vortex lines Leap-frog vortex rings Viscous relaxation towards steady ow Problem 9.1 21 HW #3 22 Summary Viscosity causes vorticity diffusion and decreases velocity gradients. For strong viscosity, viscous forces balance pressure forces. Drag coefcient scales inversely with Reynolds number as expected. 23
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Columbia - APPH - 4200
APPH 4200Physics of FluidsReviewOctober 21, 20101.!!Review2.!Problems from old Midterms3.!Midterm 20081Review Introduction Tensors, vectors, symmetric andantisymmetric tensors, vector calculus,Gauss and Stokes Theorems, Streamlines, path
Columbia - APPH - 4200
APPH 4200Physics of FluidsWaves (Ch. 7)October 28, 20101.!!Waves2.!Linear gravity waves at a free surface1~)"\".)~"X'-~cli:'0~.~1~l-.Wave (Helmholtz) Equation'41 N~ 'J"t' r"VII(' l"n~'-I'"'P",tJltX'-4Ii,.~~
Columbia - APPH - 4200
APPH 4200Physics of FluidsInternal Gravity Waves (Ch. 7)November 4, 20101.!!Review of Surface Gravity Waves2.!Linear gravity waves within a continuouslystratied uid (Buoyancy!)1Ripples2~~to~J~~r.~.J\'IrtoJ,J\:~~~\uWave Equ
Columbia - APPH - 4200
APPH 4200Physics of FluidsMore Fluid Waves/Instabilities (Ch. 7)November 18, 20101.!!Tides2.!Jeans instability1TidesThirty days of tide heights at Bridgeport Connecticut U.S.A. as calculatedfrom the Harmonic Constituent data aligned with 0h Su
Columbia - APPH - 4200
APPH 4200Physics of FluidsMore Fluid Waves (Ch. 7)November 16, 20101.!!Phasors2.!Surface Tension3.!Capillary Waves4.!Rayleigh-Taylor Instability5.!Sound6.!Organ Pipes7.!HW 41e"~"J(l~,~\f~'l~ 'I~J.J!1~Jlq:~Q,.I.~.~
Columbia - APPH - 4200
APPH 4200Physics of FluidsFluid Instabilities (Ch. 12)November 23, 20101.!!Introduction2.!Bnard Thermal Instability1~.~v-J-"'~lU'lQ~~t-~~~i'0't~.i.Equilibria can be Stable or Unstable,-.'* 'u. '0~~l"'" '- .t""\U
Columbia - APPH - 4200
APPH 4200 Physics of FluidsFluid Instabilities (Ch. 12) November 24, 20091.! ! 2.!Kelvin Helmholtz Instability Centrifugal InstabilityTuesday, November 24, 20091Kelvin-Helmholtz InstabilityTuesday, November 24, 20092More BeautyTuesday, November
Columbia - APPH - 4200
APPH 4200 Physics of FluidsA Few More Fluid Instabilities (Ch. 12) Turbulence (Ch. 13) CD December 1, 2009i-.~ .~_~_~m_.-.D_~(c._~.-~.E.-~-l-s.-c:-~-,-/jQ-lL~a.lJ-l'- C-~,F.1.! !Viscous boundary layer and waves Stability of Parallel Flows2.!t-3.!.
Columbia - APPH - 4200
APPH 4200Physics of FluidsBoundary Layers (Ch. 10)December 7, 2010Answer: A pioneer in the mathematical development ofaerodynamics who conceived the idea of a uidboundary layer, considered by many as thegreatest single discovery in uid dynamics.Qu
Columbia - APPH - 4200
APPH 4200 Physics of FluidsReview December 10, 200923 Lectures > 700 pages of text1Lecture 3 Velocity gradient tensor, strain, rotation2Deformation and Flow: Translation, Stretching, Pinching, and Rotating3Simple Comments about Velocity Gradient
Columbia - APPH - 4200
Lorenz ModelAPPH 4200 Physics of FluidsColumbia UniversityIntroductionIn 1963, Edward Lorenz modeled the nonlinear thermal convection in 2D. This is the Bnard Instability. Lorenzassumed spatial forms for the convective flow (i.e. "rolls"), the temper
Columbia - APPH - 4200
2007NRL PLASMA FORMULARYJ.D. Huba Beam Physics Branch Plasma Physics Division Naval Research Laboratory Washington, DC 20375Supported by The Oce of Naval Research1CONTENTS Numerical and Algebraic Vector Identities . . . . . . . . . . . . . . . . . .
Columbia - APPH - 4200
Numerical Solution of PlaneIrrotational FlowAPPH 4200 Physics of FluidsColumbia UniversitySolve Laplace's equation for the streamfunction, y[x,y], for two relatively simple examples. Since Mathematicacan solve thousands of simultaneous equations quic
Columbia - APPH - 4200
VOLUME 91, N UMBER 10PHYSICA L R EVIEW LET T ERSweek ending5 SEPTEMBER 2003A natomy of a Bathtub VortexA. Andersen,1,2,* T. Bohr,1 B. Stenum,2 J. Juul Rasmussen,2 and B. Lautrup31The Technical University of Denmark, Department of Physics, DK-2800 K
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 1Question 1Consider the two-dimensional, incompressible owu = (u, v, w) = (cos t, sin t, 0)Give a complete description of the streamlines and the trajectory of a particle releasedat the origin at t = 0.Extra cred
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 2In Chapter 4 of Kundu and Cohen, please do problems 6, 7, 10, and 11. Make anyassumptions you nd necessary and reasonable to solve the problems, but please statewhat they are.1
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 31. Show that for an axisymmetric, two-dimensional ow with vorticity distribution = (0, 0, (r) in cylindrical polar coordinates (r, , z ) (where 2-dimensional meansno motion in the z direction, and no variation of t
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 41. Kundu & Cohen, Chapter 7, Problem 1.2. Kundu & Cohen, Chapter 7, Problem 2.3. Kundu & Cohen, Chapter 7, Problem 4.1
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 51. K&C, Chapter 8, problem 2. The correct answer for the velocity in the wind tunnelmay seem unrealistic, and strictly, would require us to consider an additional nondimensional parameter not discussed in class, but
Columbia - APPH - 4200
APPH4200 Physics of Fluids: Homework 61. Do any one problem from K&C, Chapter 12, Problems 2, 3, 5, and 6.2. Do any two problems from K&C, Chapter 13, Problems 1, 2, and 3.3. K&C, Chpater 13, Problem 54. K&C, Chapter 13, Problem 105. Do any one probl
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Columbia - CIEN - E1201
Dartmouth - ECON - 20
Limited Dependent VariablesP(y = 1|x) = G(0 + x )y* = 0 + x + u, y = max(0,y*)Economics 20 - Prof. Anderson1Binary Dependent VariablesRecall the linear probability model, whichcan be written as P(y = 1|x) = 0 + xA drawback to the linear probabilit
Dartmouth - ECON - 20
Multiple Regression Analysisy = 0 + 1x1 + 2x2 + . . . kxk + u2. InferenceEconomics 20 - Prof. Anderson1Assumptions of the ClassicalLinear Model (CLM)So far, we know that given the GaussMarkov assumptions, OLS is BLUE,In order to do classical hypot
Dartmouth - ECON - 20
Multiple Regression Analysisy = 0 + 1x1 + 2x2 + . . . kxk + u4. Further IssuesEconomics 20 - Prof. Anderson1Redefining VariablesChanging the scale of the y variable willlead to a corresponding change in the scaleof the coefficients and standard er
Dartmouth - ECON - 20
Multiple Regression Analysisy = 0 + 1x1 + 2x2 + . . . kxk + u6. HeteroskedasticityEconomics 20 - Prof. Anderson1What is HeteroskedasticityRecall the assumption of homoskedasticityimplied that conditional on the explanatoryvariables, the variance o
Dartmouth - ECON - 20
Multiple Regression Analysisy = 0 + 1x1 + 2x2 + . . . kxk + u7. Specification and Data ProblemsEconomics 20 - Prof. Anderson1Functional FormWeve seen that a linear regression canreally fit nonlinear relationshipsCan use logs on RHS, LHS or bothCa
Dartmouth - ECON - 20
Panel Data Methodsyit = 0 + 1xit1 + . . . kxitk + uitEconomics 20 - Prof. Anderson1A True Panel vs.A Pooled Cross SectionOften loosely use the term panel data torefer to any data set that has both a crosssectional dimension and a time-seriesdimens
Dartmouth - ECON - 20
Review of Probability andStatistics(i.e. things you learned in Ec 10 andneed to remember to do well in thisclass!)Economics20Prof.Anderson1Random VariablesX is a random variable if it represents a randomdraw from some populationa discrete random
Dartmouth - ECON - 20
Simultaneous Equationsy1 = 1y2 + 1z1 + u1y2 = 2y1 + 2z2 + u2Economics 20 - Prof. Anderson1SimultaneitySimultaneity is a specific type ofendogeneity problem in which theexplanatory variable is jointly determinedwith the dependent variableAs with
Dartmouth - ECON - 20
Economics 20Prof. Patricia M. AndersonStudy Guide for the MidtermThis is not meant to represent an exhaustive list of the knowledge required to do well on themidterm. Rather, it outlines the major areas weve covered, helping you to pinpoint areas wher
Dartmouth - ECON - 20
Economics 20Prof. Patricia M. AndersonFinal ReviewBinary Dependent VariablesUsing OLS on a binary dependent variable is referred to as a linear probability model (LPM).The biggest problem with a LPM is that the predicted values are not constrained to
Dartmouth - ECON - 20
Time Series Datayt = 0 + 1xt1 + . . .+ kxtk + ut1. Basic AnalysisEconomics 20 - Prof. Anderson1Time Series vs. Cross SectionalTime series data has a temporal ordering,unlike cross-section dataWill need to alter some of our assumptionsto take into
Dartmouth - ECON - 20
Time Series Datayt = 0 + 1xt1 + . . .+ kxtk + ut2. Further IssuesEconomics 20 - Prof. Anderson1Testing for AR(1) SerialCorrelationWant to be able to test for whether theerrors are serially correlated or notWant to test the null that = 0 in ut = u
Staten Island - PHY - 116
CHAPTER 1: Introduction, Measurement, EstimatingAnswers to Questions1.(a) Fundamental standards should be accessible, invariable, indestructible, and reproducible. Aparticular persons foot would not be very accessible, since the person could not be at
LSU - MICRO - 1011
Microorganisms and ManBiology 1011Syllabus BIOL 1011, Fall 2010 Lectures: Mon. and Wed.3:40 5:00pm INSTRUCTOR: Dr. Randall (Randy) Gayda OFFICE: 518 Life Sciences Building OFFICE HOURS: MTWTh 12 3 PMor by appointment.Required Materials Lecture
LSU - MICRO - 1011
Lecture 3Chemistry FundamentalsAtomsElementsElectron ConfigurationsChemical BondsBasic type of Chemical ReactionsBiological Molecules Inorganic w/o carbon Water and its properties. Organic1. The structure of atoms Definition of an atom. Parts
LSU - MICRO - 1011
Lecture 4Biological Organic Molecules A. Organic Molecules Why carbon? Functional Groups Composed of subunits Building Blocks. B. Major Biological Molecules Carbohydrates Lipids ProteinsSelf-Tests A bond formed by sharing electronsin the outer
LSU - MICRO - 1011
Lecture 2 - OutlineDevelopment of MicrobiologyA. Discovery of microorganisms is dependenton microscope.B. Experimental science removed belief inspontaneous generation.C. Early observations relating microbes anddiseases.D. The Golden Age of Microbi
National Taipei University - EECS - 000
Punctuation and MechanicsWriting Paragraphs/Thesis/Outline1The Living End: The Period (.) The period is the red light at the end of asentence. When you reach the period, it's all over. Whatever thought you were trying to conveyhas been delivered.
National Taipei University - EECS - 000
General-specific TextsTask One: Selling Cities: Promoting New Images for Meetings Tourism1 Meetings tourism, which we define as travel associated with attendance at corporateor association meetings, conferences, conventions, or congresses or public or
National Taipei University - EECS - 000
General-Specific TextsAudience1AudienceBackground knowledge presumedBackgroundText A targets an educated, but not highly specialized,audience.audience.It provides a lot of background material and is carefulto avoid too much technical vocabulary.
National Taipei University - EECS - 000
A.1 People have been pulling freshwater out of the oceans for centuries usingtechnologies that involve evaporation, which leaves the salts and other unwantedconstituents behind. 2 Salty source water is treated to speed evaporation, and theevaporated w
National Taipei University - EECS - 000
Numbers
National Taipei University - EECS - 000
Technical WritingSeptember 16, 20111 September 16 Orientation September 23 Paragraph and essay writing;Punctuation and mechanics September 30 Features of Academic/Technicalwriting October 7 Writing General-Specific texts;Audience October 14 Writ
National Taipei University - EECS - 000
Features of Academic WritingAnd What is Technical Writing1Why write a research report?A research report is a paper written by aninvestigator to describe a research studythat he or she has completed.thatThe purpose of the report is to explain toot
National Taipei University - EECS - 101
123
National Taipei University - EECS - 101
Use the circuit in Figure 1 to supply a variable voltage to a load of R=5. The source is 120VRMS, 60 Hz. The load power has a maximum value of 2100 W and minimum of 500 W. Find:a) the required range of b) the SCR average current requirementc) the curr
National Taipei University - EECS - 101
Tsogbayar OnhProblem_1A buck chopper like that in Figure 7.1 has the following data: E=40 V, T=50 s, L=250H, D=0.4,C=60 F, and R=10 .Find:(a) the value of L necessary for the continuous current mode(b) VC(c) Imax and Imin(d) CVa) TR 0.00005 *
National Taipei University - EECS - 101
O.TsogbayarHomeworkProblemA dc shunt motor drives a centrifugal pump at a speed of 1000 rpm when the terminal voltageand line currents are 200 V and 50 A, respectively. The armature and field resistances are 0.1 and 100 , respectively.(a) Designe a
National Taipei University - EECS - 101
SUBJECT1.2.3.4.5.Diode Single-Phase RectifierSingle-Phase Bridge Phase-Controller RectifierSingle-Phase Bridge Phase-Controller RectifierSingle-Phase Bridge Phase-Controller Rectifier and DC Load VoltageThree-Phase Half RectifierSINGLE - PHASE
National Taipei University - EECS - 101
DC LOAD VOLTAGESome circuit arrangement effectively place a DC voltage in the circuit as part of the load. This mightresult from capacitor voltage, another source may be the back electromotive force (EMF) of DC motor.As shown, if the inductor is ideal