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Unformatted text preview: ME ED 240 Fluid Mechanics
Fall 2004
FINAL EXAM Name 50 \‘ Instructions: Show your work, partial credit will be given only if there is sufﬁcient detail to the
solutions Read all questions carefully. I. (25 pts) True or False / Short answer TorF F (a) Fluids and solids have the same relationship between stress in the material and strain. Ir , (b) The Reynolds transport theorem describes the relationship between the lagrangian and
eulerian descriptions of ﬂuid ﬂow. F (c) The ﬂow just upstream of a normal shock is subsonic. T (d) The Buckingham Pi theorem is used to determine dimensionless parameters that can be
used to simplify the analysis of ﬂuid ﬂows. v< (e) Turbulence can help to create separation in external ﬂows. (i) For steady inviscid ﬂows, the continuity equation and energy equation are redundant T i (g) Friction and shocks in compressible ﬂows are both sources of the loss of energy. ln (h) In general, the drag produced by an external ﬂow around a body is proportional to both the
volume and weight of the body. T (i) streamlines, streaklines, and pathlines are all the same thing in steady ﬂows F (j) Minor losses in pipes are proportional to AP2 ‘ 1. con’t Short answer 4, 7) (k) describe the nature of a boundary layer in an external ﬂow. What is the physical interpretation of
the displacement thickness? ‘ ‘ a in ,MY 'tmﬁmM/w/‘Z’i—m may/7) ﬂu new ‘ M if”: ut.
ﬂamzkm w? mew/M :3]?
% any/MM ﬂwcﬂrnezd’ 5" M‘aM/wam l
m m fay/M ital/745 mamwfzaw MM _. 63 (1) determine the ﬂuid convection in the x and y directions for the velocity ﬁeld V = x2 f — 2 x y] t + : ' K o 2 3
9“ “,9” vi“ )< (1x3 02 3C ) ’2“
2 ‘6‘: “3¥+Vg§ 3 K2413) Jew2x) 2 ‘2’}? ‘F “a? 3&9“— (m) in your design project, what was the theoretical basis of the connection between the pipe system
@ and the given pump? @ @ (0) describe the hydrostatic variation. of pressure in a ﬂuid. '
4”” m m M 4m 91%st Mpwr w E7 W arwyﬁﬁgﬂ m. s l3 2. (20 pts) River ﬂoods are typically held back levees. During large storms temporary barriers
are used in places without levees. .One manufacturer has barriers that weigh W and have a
length L and have other dimensions as shown. The principle is that the barrier resists the
water with the force due to dry friction between barrier and the ground. Recall, that force is given by Ff = 77 N where, N, is the net normal force and 77 is the coefﬁcient of static
friction. ' t. t ‘1 Assume the water has a density, p and that w 3;: atmospheric pressure cancels all around the
’ barrier. Considering the hydrostatic force acting on
the barrier, derive an expression for the I maximum height of water h that this of“
. ~.‘ ‘
7.. a
11),. \
vbwz‘,‘«¢ ‘ .‘ . .‘w x U “n. ) (LA F, :u "" 4'pr x 3
€9§$ w teawugmwi' W at 3mg 0 @
‘ \.',_ L— K d! [9130 N “N "FrCO'SG'ZO ﬁrms} manufacturer’s barriers can hold back.
(draw a free body diagram) Wmth “YIN >$>§Jh9 stingzo “ N f ' L M _:
69 M f3 (imagxa St 96.939 0
§a\u.c lav N w w W 9% at gaammmum (mt. fvéi, Wr_£3’l/_VL (050. in?” WZO' SNML‘QW’A. 3. (20 pts) Recall, Couette ﬂows are an exact solution to the Navier—Stokes equations. In this
case, water (,0 = 1000 kg/m3 ,,u = 0.001 N —s/m2) ﬂows in a H = 25 mm gap between
two inﬁnitely long plates as shown. The top plate moves with a speed U a, = 0.01 m / s and the bottom plate is stationary. Two pressure gages are used to measure the static pressures at
point 1 and point 2. The distance between the pressure gages is L = 0.15 m U°° ’ For steady ﬂow between the plates, the velocity is
" “ ‘ given by, u(z) = Um i+—l—(a—P)(z2 —zH)
H 2;: 6x Determine the height above the lower plate at which the
velocity will be maximum if, dqcv 2129; 94m edges am: 4. (20 pts) Before the Wright Brothers ﬂew their airplane in 1903 they worked out the details of
their design by ﬂying kites. An example shown in the ﬁgure has a weight W = 220 N and is
ﬂying in a U 00 = 40 km / hr breeze. In this wind the kite line has a tension of T = 60 N and the line is at an angle of 0 = 30" relative to the ground. The properties of the air are ,
p =l.2 kg/m3 and
,u =1.9x10'5N—s/m2 Assume that the liﬂ and drag produced by
the kite are both proportional to the planform area of the kite Ac = 7.5 m2. The wings of the kite
have a chord length C = 1.5 m. W) Z QOW/hr> z mwis . a.) Draw a free body diagram and determine the lift and drag coefﬁcients for the kite. L“ EQUIUBIZHMA Zazo 2' D’nge ﬂ DZ'TCOSG’
7” ZgazwL—w —Ts.,:,.e lel/tmfsz‘ne L19
w A D2 (90065500: 5/99” r
*5 L. 2 220M + (towsmaw =2§0N
OWL}: 15"“ ' 9 0.240953”
if) “0 ’40 L0‘1%%>(M.l(nfs)1(7,(mz) ‘ b.) If the ﬂow does not separate from the wings of the kite and assuming the wings can be modeled as
a thin ' the dis lace t thickness of the b0 er wing at the /’9)(/0'$/N’f/V7L '>/()S J1, W M“ vay [email protected]+b$x 192:“ Wm Xac
00:3» 5. (15 pts) You are standing at sealevel and watch as a high
altitude of z = 3000 m The pilot radios that he is ﬂying
temperature outside the airplane is T = 100 C (a) Under these conditions when do I e airplane? (circle (1) (2) Before it gets to above where
you are standing. At the time it gets to above After it passes over where
where you are standing. you are standing. @e answer to part (a) is either (1) [email protected] estimate the time either before or after the plane passes directly above that you hear the plane.
~ ’I
z L —~> ﬂ 2 2% [.1 )
Ma, 4Q, ...
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 Spring '07
 SONNENMEIER,JAMES
 Friction, 1%, Wright brothers, WZO

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