Lecture-8 - APPH 4200 Physics of Fluids Problem Solving and...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
APPH 4200 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1. Quick Review 2. V o r t i c i t y 3. Kelvin’s Theorem 4. Examples 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Ç"Tt=l ~ I $T1P#( ç-r;: ,#3 Ç(¡i it l+ Ç'7E rP t: ç- D iI;4 Lv A fJ t c.t u /Z t2 ~ tv (L (TE p Ô t- /V A- L- L I~ ~ ò C- A. 6 E 0 J/ £-rlf A I' io f-OJi c. ( "- '1 S _ r ç TH i S A 1) T ¡v A. ,CA-L ¿) t1 çrTI ( f If ¿i ~ '- E. . ? ~ ~ ~ o~ TOY /VA t- (c .) A il l' ç (. L ve.L (J -t L( .l ~( 7 A--- ò~ a~ L lÍ ~ S' t) TH &2 \.' ': 0 l2 (¿ &. ..A ~C¿)) lj rf c A J) e Å."- '- 1- t~ P Yl () -1 c. c."" ~ rl t7 Âd (. c. lf r1 c).l tf ,c t F l'c ( C U t- 'r . ç Ec.tZLI -lK ;10\7 ~C)".vEf'(tE4Â7 LOù.l~/.-A-~ ç (" S Te p. . C' A. -r ~ C 01/ ¡J L( A. t=A- cE 0 d /ê ". r A. .A~ S / N /Tle/'0 i x. (J. ') N¡i L '( GO;. S E-I? V iA(l Ò A- pI! ( ~ C ( ,oL C S rk 0 -' IS.- T "" ".1 #/V '7 v l ~ "'Ò '" ;£~ (v ~r E-"IS ft-' r ) p Il ( __ c ( to L If (è ~ò Â, Ç( pf.;AJ C tAr\ Y ()v CJ- A- ç . i It A- i/ ~ c-GQ òi,J L L L f S Y¿L)/l SDLU(fdl--: ftiL l ( t- ¿ l!J /Z / A.u ,7' è) ., How to solve fuid problems? (Like those in textbook) 2
Background image of page 2
Mechanical Energy Density for a Stokes Fluid 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
i 'V \ ~ Nl"ì I .'" \£t C0 -i \l" 1'J 0 l~ -l'" .. + \l ,, ~~ J /' - IltJ 10 I" ,- (1 ì! () l t i. Qj tLl '- il li) \. -- q" " \ i :) 1'3 L I- re Q \t b 1- I~ . u 't I :J a , \j J' f- 1, 'x i cd ') Ii , , ~!J Z '" .J VI ~ , "'\ -i l:: \ -l r W\ -t 'J II ¡: ClO ~a. ~O- Q Q 'V a- lJ CL It: '; ! ") q, ti s: (- v- IJ v 1 ). VJ "\ :¿ C! i- '\ \/' :: '-- l: I.L 1 )- (/ , ci "; I.. "' \L ; ~ .~ l:: J ~ ~ ll V' q; -0 Vi cv Fluids Equations ( internal ) 4
Background image of page 4
r¡r- -i \ i :J ~ ../ i~ . J -If' t "t - I :: 0 Il\ ~ (' (U .j , + ~~ vA l/ -i (V \~ '-,f' () (\ -- ,J Q I 'X \\ l '.. l. lL II L I\: l=- I~ b. Z /' 1: "= -l-a I :J F ?$ i \L ù I tr ' \ y. lrJ 'J -. r- 1~ .J 't -: 1:5 '- v :i .. ,~ 13' l~ X 1- 'j )- b- el "- )~ f- 'C 1"3 \-. \~\ .u I~\~ (" ~ 'I (ò C' \ c: 1/ Vorticity Dynamics (Remember the importance of viscosity.) ∇× ( A × B )= A ( · B ) - B ( · A )+( B · ) A - ( A · ) B 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
.. ~ i 0 y r- , ¡:. . 1: Q ~ F .. ~ II Q * Ç) ~ 'i V\ - lL )l :, J :i -; ,.. tJ \J L. .~ \D \I 'f "" " tl l \1 c\ ~ . ~ l. k j ,'- ) r l( '- j w \ i rv ,. 1 iv
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 28

Lecture-8 - APPH 4200 Physics of Fluids Problem Solving and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online