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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 + 'vVV 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  (Ir0( . I I . In,“ .
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1 Name EM‘f’Y‘tbn 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
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t
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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 twodimensional 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).
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 Spring '11
 Wereley

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