mt1soln - ale *5 #145467 FOR NO CREDIT FOR 7 ANY MATHEMch...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ale *5 #145467 FOR NO CREDIT FOR 7 ANY MATHEMch ERRORS D\MENS‘OMAULH’ iNCoRREQT IN unfit: . uxbmc‘ - UNIVERSITY OF CALIFORNIA, BERKELEY MECHANICAL ENGINEERING _ .r. ME106 . Fluid Mechanics - NAME QEizELLlEES lst Test, SOB Prof S. MOMS 1.(65) (a) Find the fluid acceleration a for plane stagnation point flow in which the velocity is given by the expression V = cmi — cyj (the Constant c > 0). - - Exam/x stats «uh—«MA Ewuaa if: z :92. text-1 __ :23; .2 ‘ Mean '. \QH . ‘5 5200 E: Q J at rt" Cw “to . 8r. ‘Dev . 37. ) : at «a , we , w N "5" N “1: ‘9 )- V's-“At: z: "‘7‘ -' ’ l d x; 3"" \' (Aya‘cj‘ Eli é-ivtfifihin-‘f _ i, I M W m E, {'53:- 5 Q9; (it: C it g :7ng A.” 3 A? > ‘ ' 3 e a e f 1:.» , x. i If”) .4 v' i or; V: UL i + ’U‘ CU} “'2 v x v N N '31] "I: 1 £1, .4 k 6} a}: at "‘T £4" £5“. :5 a E I! d" J fit“ a A A L f . ' 4 "X g \ at) C 2w ,, - . , M" / '1 ,1; ~; :2: -' M“? V 5% 3‘ u. r‘ 31‘; ' ‘— -..z m» amww . ‘3? i 5! 1" I i L051: mm it» . ~ mot'H/l eMY‘Ca/‘SI "'5_ why“— ctt'd not Undefime, uhfl' m5) *- 5 CCWQAOQ. . vac-101‘s amok $CQlOU’5J - 10 (b) By considering the stagnation streamline, explain why a 7-5 0 in this flow. a EA . \. f I L; w 35%,“? Iva~f’5t,min a: ctr i if?“ zit-"fl W-” ‘ ‘- «-‘r in": .2 ' ::- " -"-‘ . \ v 3’ ; "\‘l 2’_LQ;,"\V ‘5. VMQQWE a,-"~&?'r«.filil 1,1:- L... “3 :3“? it“ “a 1‘ _ r I . t , ' :54; «Lilia-“t. diet-1’} as i?" U‘ ND Orcdx-lr 9w vagumewie 4mm- ! - ' Phlébi'c.a\ mm‘ IN BLOCK LETTERS PRINT YOUR NAME ON THIS PAGE “9 1508—1 2. (65) The vector field V : iécrf—F-vfi‘, 2367+ c212 {c > 0, constant) stretched in the axial direction. For this flow, the fluid acceleration is 2 a= (ice * 3:)H (9‘1 e if? at ’1‘ WKQ Swag Mam/1‘. LiOQ/(of) a» Dex/'- 332A represents a vortex that is being given by the expression )é + 62217:. (You are not required to Show that.) Find the partial differential equation satisfied by the function v(r, if). (You are not asked to solve it.) Given. In cylindrical polar coordinates 136', 2, if F : frf' + fag + fzfi is an arbitrary vector1 then » wJun 61"": 5m 3 i E I 61 Z § p. z i i Z ‘1' T V “2'1 54L {A {:7 M, V ‘9ch ‘ ~36 “1 $1M attempkeci to Eula“? CCIUQhCV" Quad \fiufltfi. ~ Em Ccefltlm L513 , 4: '50 1808—2 cm at smut-H04 I Pod/rt Wat-“(One 1 —- Did Vick ace vi. 912 o midi“ - ML‘S‘aM% v“ tom/13) —- 5)— ? 7‘9 3:: ' ¥ 5‘ 3 3 fr TfB fz r s “7;. (w 2;; ,h “r Iii” ‘y ’ p 1;": , 3:4 I“ {Lizzy} 1'" e V"- T—1 #7:. ‘ r?»- V‘ ii i b g L. Di. v x . Z; <— + .2 W_WWWM__W'N£ v+w Expanding V “9 '2 C3 5 1,; w» i , 1%; - " m3. :- T in: m L: ‘I‘ 3. vi (“a V; 3,. 1‘ C‘ "r 5- ' h -. g 5 Jr \6 the CLWPlE’i’t and " _. (1 fit {it 70 3. ('35) The figure shows the side view of two discs each of radius R, and separated by fixed distance h. Air enters the gap between the discs with speed Vb through the supply tube of radius a, flows radiain and leaves as a free jet into the atmosphere Atmospheric pressure is pa. Within the gap, the Speed V varies with distance r from the axis according to the rule v={ (You are not required to show that.) The pressure within the supply tube is unknown; it is not atmospheric. _ hm Ax isymmclric ,1; HQ QM- v:UOJ?”-"? WOLdM “3/ CM” I'i V0 ifr<a 2V0 ifr>a. s. l. ssh—- rah—- kin .q Atmosphcl'c ‘a - U '— r "_ frecjel e ’9‘ W id, ": Wynn J 83% .3 L93 v Bfch C) Go 4' 5 £0?“ a. Au—nospl‘mm|a 0 Cog . vm P Wm (LUZ? (3.) Using the Bernouili equation, find the pressure p within the gap as a function of r, p, Vb, h and a. W Sketch p as a function of 7" showing clearly any maxima, minima and zeros. (You need to consider the cases 7“ < a, r > a separately.) 4' ‘ “Pr g ' \ + 520 For WW5 ‘ "" -' - 5 ' t;qu wagon ewe/We “Tl/\L‘S welt/idea Haase. who +0 'de Pew‘vg gay-ea. = tr: —- , ‘ _-_- - f”; 11.. 5 v 1508—3 .7 a“? R a +5 ‘Er caveat a *7 \ pm; 100,. amen“ 45 \Moalmgl Jr WW5 go 3 (b) Noting that the flow is axisymmetric, derive the integral expressing the force F exerted By the air "70 On both sides of the lower disc in terms the pressure difference p(r} -— pa. Pi: ’- ‘7 I, “r 3 1;” "9"5k-5w‘--I.o *2 3 ' w iii. 1» ' flautRE _ 7 | 7‘ _ 1. ,7 FOR mu. ORbe ‘ W 0U“ ' W4“ 46? Wt“ YZETM-w‘ ' 77,777 m WW“ m » ~--‘--w~-'-- -— ‘---~Wr~ _i Ifiwiw__'flfifl_r_fi):‘E——H_MMJ fit“, A“ j“ y ‘M" r ' SE ; ‘2 1-” 5 , . WU; 3 “1 3h _‘ If , a. ‘7. . .: - . n I 091‘? “affix, : ‘ I “g f, \ jg {x (c) Hence show that F is given by the expressionk m‘l‘ k.) H \O 93v can“: (9 1‘ 3.. Fan...) Via-1N mammal? . a4 R Explain physically why, despite the presence of a stagnation point at O, the force is upwards if R > a. (2 ksk K; .24, s r-—-»-—."-—’_'-— a 1L aft \ J ,Q J é 3‘ a “w”. w 5f; rev-m! 1 e in +5 _ 1508—4 emu W smwame prB "3:? $30; , OW mask 0’? m, dxeic we, (stifle-Poe wees amsewmim. FCRMM, as war, v” dean ' memes, be We W Pa 0* sac-n paws _ 4’01" - v“ 5 CA - - ...
View Full Document

This note was uploaded on 04/29/2008 for the course ME 106 taught by Professor Morris during the Spring '08 term at University of California, Berkeley.

Page1 / 4

mt1soln - ale *5 #145467 FOR NO CREDIT FOR 7 ANY MATHEMch...

This preview shows document pages 1 - 4. Sign up to view the full document.

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