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exam1Solution - Fluid Mechanics II Examl Name: Score 1 A...

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Unformatted text preview: Fluid Mechanics II Examl Name: Score 1 A particle moves along the horizontal centerline of a converging channel. The velocity at the centerline of the channel is given by 17 = V1(1 +f)t, where VI and L are constant. Find an expression for the acceleration of the particle. (5 points) .3 d? )Tf —-* 4‘ all? 31? a?! (3?? or r (at + 'v-VV- n + an War“??? r‘ n _‘ Y5” :r flighwmjmt— Loni 2. The Reynolds transport theorem can be written as DEW—6f de+I bV‘dA or "at p p '71 Cl? CS Where bis the intensive property and B is the extensive property. Explain the physical meaning of each term and show which term employs Lagrangian description and which term uses Eulerian description. (7 points) ' a " " " . -. .. L-. , 4b“. {We “(aft 0% char]? b 0900:0th wqh S‘then, Lfi3wajmq 'D't re r I _ I H - (Ir-0(- . I I- . In,“ . e ‘ {.9}er {he tune (at: 0-? Chm}? 0'; {'9 G j waifd w H\ CV“ in: We .9 C; {V l ___,,..—- a _ TEL-delta n I "" ‘dA. Mfr-1% b on the thrat ST-qw due h {M ‘ l 1 Name EM‘f’Y‘t-bn 3. One velocity component of a two dimensional incompressible flow field is given by u = 2xy, find the expression of another velocity component. (7 points) "‘ a [t if 2D Tflfmptrm'b‘e silent :0 at w ’ )l1+-E:j':o fl— w. my"? 4. The two components of velocity in a flow field are given by u = 3’2 —x(1 +x).v = y(2x + 1), ‘Wo’cahunat is this flow irrational? Show your work. (6 points) a "3’ 3 -;(§L§ml_ al'tz—vnmij) “1 ‘2'" a; an 2- 31 “yr—— 2 Name S. A flow field is described by the equation V = (3x2 + 1)? - 6xyj‘, determine the following (i) the volume dilatation rate; (ii) rate of shear strain (or angular deformation), and (iii) rotation. ('12 points) . r _ - W F .,_ ".- \f I _ - — v.1. L ..r_ g f ‘1' l ( {It} _ r If r l 3‘ E -r\':" "' h if! _|‘{ i'fl' -\ I K- - '_ 3.! l _: .. ' Fr. “'1‘! ' ' ' . F ._ - - .. ." ‘3 {if}. . r I '--I {J “r h I} ) h- ;4 'l ‘ ‘ II J .-._.\ - 2 F '=' "J k 6 Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetter surface as shown here. The region of reduced flow is called boundary layer. At the leading edge of the place, the velocity profile may be considered uniformly distributed with a value U. All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also U. If the x direction velocity profile at section (2) is a - [3] Develop an expression for the volume flow rate through the edge of the boundary layer from the leading edge to the location downstream at x where the boundary layer thickness is 6. (20 points) .' . W _I_.4 _. . W. . .. W ( ; II section (1), U .. IS?°ti°“(2) L . n l_ 'U _ . f“ If l l I l l l I t l I it ' J r. 7 A liquid flows down an inciined plane surface in a steady, fully developed laminar film of thickness of h. Assume flow is two-dimensional 1. Give your assumptions (4 points); 2. Simplify the continuity and Navier—Stokes equations to model this flow field (8 points); 3. Find expressions for a. the liquid velocity profile (10 points); 1). the shear stress distribution (4 points); c. the volume flow rate (10 points); d. and the average velocity (3 points). 4. If the film thickness h=1 mm and the plane inclined at 9:15”, find the average velocity (4 points). If I fif’fifi‘fj'i -- . I _ a.” _ A V II: 1 d devede 307‘ 7.7 e o 69) mcmpmmte ® iwo dr-m w: 0 ’ ® L0 If“ "LIA {1T LEW,— ‘ ' h" C"? a? 1;": M,- up be V30 6,}: - r r» -‘ n - — — v —- a»: . Q 8,10,, 6 .7. b "7 0 g) : ‘ l . l. ' ermfi‘lbm 5""? Page“? 4 M V 4 \76% : —%+/6'{ ‘a " ’ <12 6 7 a a ."l :' 4 ' ‘- —-—--------—~ 1/1 ‘4V f3L3)” 5:] “P/Ml 2-+ 5 Name CINZ'W‘Wr 91mm“ “'9 hm" . fl— y = \ -3 VI’ “figro T“ #ufla V': But V30 {0! V73”ng 0'1 JD“? N‘H- V: 0. iv Ffum {he 1’0“ng e‘iuab‘m 1% T—ofirpcffm W? knw-v 3” a’u ) -. 'W‘F/“W ~+ [933:0 => % z/Lq—fig.+ {>31 TM» left We is a fwcbm «F “r and the 193% Rob 11‘ afwbh b “f 2f.- Uggtzo), 5‘0 fit: (:va Becafife {*9 Wm”? 9+“ mfg” fl “WW (Batu) WP {Tet 2.13 = 0 $0 the Muménkvm 919‘“th Can he ffianl.‘ed a} at“ am (MW/a m1” {flwflfinm --® ') ' aP —%+%1:O *W‘ pfiawzo ——-@ ...
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exam1Solution - Fluid Mechanics II Examl Name: Score 1 A...

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