# set12-answers - 6.7 For a certain incompressible...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.7 For a certain incompressible, two—dimensional ﬂow ﬁeld the velocity component in the y direction is given by the equation ' U=3xy—x2y% Determine the velocity component in theix direction so that the continuity equation is satisﬁed. ‘ 72> Sal/37% 771? cvnéliﬂiaiﬂy 9550:2955 __ ——-“— (I; 3-,, 1 \$31? ll Eguaiz'o/J (2) can be Mﬂyméw/ th raped £0 2: -/o ain‘th [4“ _~_ _/.\5)(¢:/X +fX’dx+f-(5) or x3 u = ‘i—xzdr 44(3) where 75(9) is an undekrmined ﬁmeézéw of g. 6J2 For each of the following stream ‘fufnctions, with units of mzls, detemtine the magnitude and the janglc the velocity vector makes with the x-axis at x = l m, y 2 m. Locate any stagnation points in the ﬂow ﬁeld. ’ _(a) ¢=xy (b) ¢=~2xz+y H déﬁhl‘flo'h 0/ ’ﬁh: afreém , 1 _; ,L‘I’ .._;.<>‘{’ : (35437)? “" 2M ’ w * “(a—J X3) ‘ , f , V 4+ Xenia/7: ﬁ/Iowig ﬁat r=~2L4f§€ 5’7‘.‘ “‘0 5” “9’9"?” “*0? “"5 “97“?”34‘mh .é/Izi'WWZW: ms raw-10.x, = - ’ » ‘ f” j E 3 :Ai- x: ) “j if Agl/aws #31411. *émd 11‘5'5% mus) ; i V S/nce Lt¢ol ﬁne/ci are Ina Jéajﬂ¢£70h [Jo/975;. +0 6.22 The stream function for an incompres- y, my sible ﬂow ﬁeld is given by the equation ‘ II! = 3ng — Y3 1.0: where the stream function has the units of nil/s with x and y in meters. (at) Sketch the stream— line(s) passing through the origin. (b) Determine the rate of ﬂow across the straight path AB shown * in Fig, P622. A 1.0' m FIGURE P62 2 ( a») lines of wad-401‘ ¢ are slra’m/Mes. V 5r % —‘ 3X2j ~73 72': 3:5/7f4/n/l/“76 Fax/)7;- fﬁmuﬁ 777: 0/2709 :0) yzo) has a Vd/m: ¢=0. 7714’s) 7718 9344:4143” for fire skew/biz: fit/wilt The air/th 115 0 = 3x 23 ~ ya or :1: i’l/Ex 4 sl’eéc/z 0/ 771356 sfrevmi/hes 13 Mow/1 in 7746 ﬂit/re. (A) _, 6»— sM 45 [5’ 96:0) 9:1,». 17mi- 2 9g smug — m3= «Inns/5 (P9, “my Wm) 41‘ ,4 15:14") 3:5 .59 7710.1! 46, = 30070) — (0)3 i: 0 ll Hus ) 49: 9% = ‘JWVS (per am't Low/“I14 The‘ nejm‘xk 5/7.” ﬁtn‘ 77/: flaw is From [Vi/It kt liﬂ‘ as £90k 14mm 24 -/o 5. ﬁéC—u23 l 6376; A layer of viscous liquid of consthnti thickness (no velocity perpendicular to plate)" ﬂows steadily down an inﬁnite, inclined plalne; Determine, by means of the Navier—Stokes eqiuai tions, the relationship between the thickness of, the layer and the discharge per unit width. The ﬂow is laminar, and assume air resistance is neg- ligible so that the shearing stress at the free sur- face is zero. led/.774 771a word/mug: 5115145”: shown /;'1 ﬁve ﬁgure : = I n p - .— 7/ OJ w— ol and from 1112 amt/mutt, egawttcw a? 40. //Ml\$, From 7776 x— (ImM/Wfﬁf 07‘ :Me A’m/m'r -5¥a/(e.s elude»; [53», 4,1274.) , J 2—21: ‘0! Efﬂ- ax quid; s/n +/u. d3; (I) 14/30) _5;'h(c 77mm is 4‘. free sunéce/ 771m Cannot! be a. Pmmre jmd/eﬂf I}: 7712 x—d/recy‘wiv So ‘fha-é :0 4,44! 5 [U can? be. tat/«1‘79?» 4: a” 3- 0/24" = *ﬂ3 who! djz 77 \$111457” :49}; y/é/KZS %5-;- m @3 What): 1!- C, (2) Slhce The Sheﬂrlhj shes—S i Q} 2.”. 73x 7‘; at: T M Gian/5, 7ero ai‘ 77m free Jar/ace. (3:4,) [£- [o/lams 7‘7mi g5;- -'-" (Li: {7 = ’K .50 771a2§ 722 60/617011 53,12) 1:5 C ,& .Slhol I /" In 147/7796” 0/ 1.55/2) y/é/is .i .97“ - ‘ _ Jar S/nte (4:0 at 3:0] v[o//aw.s ﬁué CZ :0) 0115/ Wereére : a _ 612 LC {Cg—d 5mg“ "2) "L 77“ f/owmfe ’0” “my: width can A: expressed as j. =/ rule; 60 ﬂat ﬂ 3 o _- A? S/nol {1635,— fﬁ/ : p376 ma 5 we a j 3/“ 0 l i l l l l . 6.80 An incompressible, viscous ﬂuid is placed between horizontal, inﬁnite, parallel plates as is shown in Fig“ P680. The two plates move in opposite directions with constant veloc— ities, U, and U2, as shown. The pressure gradient in the x direction is zero and the only body forice is due to the ﬂuid weight. Use the Navier~Stolies equations to derive an expression for the velocity ‘ distribution between the plates. Assume lamiriar ﬂow. 1 FIGURE P630 l x i i E Far ﬁve. Sfecx'f/éc/ Candy/7M5) ’V’=0) “3% 35:91 4”"! f2: =0 ‘50 ﬂat 777‘ x'wmf’o’lpﬁ‘f 075 ﬁre IVﬂV/é’k‘S'lkaJ‘ (744154,” (Eg‘é,/Z7£) reduces £0; J (/2 d;: i0 ‘0 Inkyaémn o% E; m yL/e/tls a: 7" (z (Z) 5,, y: o ) Aer—JD;3 ana’ ﬁre/e5”: 79w» 57,62) 1:»; E F5!» g: b) “=0, 50E 7774f 15 = (jg —Z& or C, — Thus) i4»e7 E” \$9 \$53 rum...“ . i: _ { g ﬁﬁéﬁﬁ 5% mews ﬂag: {ggmgiﬁs migh; : 3%} ibﬁﬁ Wages» “ === 33.633 1% ~ 3&2} i3 ﬁanmmaé @meeﬁ mm éﬁ‘ﬁﬁiiﬁ, 3mm“ ' Emmi pamﬁai giazass 33 Shawn ﬁzz 'igig. P2183; The flask? maws : bgtwem 3313 3313335 unda me action of a pmgsum gmaiiéem; anti {has uppm‘ piaic movag whiz a wallmciiy if whﬂe this bamm mam ' is mm? A Limbs maﬁamsﬁgr maximized beiwsm {gainm akmg 3% Emma; iindicams a giiffemnﬁaﬁ maﬁng 0? {2.7: ism. if {Em : apper- pﬁam mums with a vcicmiiy @f {162 Iii/5? a: win: dis'zmcc i {mm {ha batman plate \$053 me;- maximum valagity in {he gap - haw-3m me mg piams assist? Agsums lamina: ﬂow” i E é s? g i g , 3 § 2‘ E g §?§Q§RE Pﬁaéﬁi‘s A 4 d “rm i f a": {‘M «g» m #5; f a .a a “j £33 ubgﬁjégwéﬂg éJiféf {WQ’XEMHM Wimffgg WW ﬂag:sz €22? fféSEQﬁEQ \$2M wﬁéwe g5“: Ziéwsg ! : é 3 w ‘? £553“? ’9 m man w. “M “g9 m “é” ‘ w d5; 4% 3% 53% Jig/23f M (swag? wag? £45? £3,613 ‘ Egg ,M; 64’? £9 g g%%% “ﬁg-ff “55% 1 l & WM 3 NW mmmgéﬂw {we iﬁgmm 3325 Kiwi}; Uf‘ﬁ ‘ﬂzj . . ..€=‘_ «\$ng “=0 '3 g E E E E E E E i E g E g E g E E” g MW“? f7 . 1m 3"“ i Q ...
View Full Document

## This note was uploaded on 01/30/2012 for the course ME 3340 taught by Professor Smith during the Spring '09 term at Georgia Tech.

### Page1 / 6

set12-answers - 6.7 For a certain incompressible...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online