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Unformatted text preview: AER205F FLUID MECHANICS and TRANSPORT PHENOMENA
Quiz 3
17 November 2006 9:10 pm  10:00 am Closed Book, no aid sheets
Nonprogrammable calculators allowed Instructor: J. W. Davis Family Name: .8 Kb bouts.
Given Name: (ml wl‘k (JV4.
Student #: FOR MARKER USE ONLY )—A
O ,_.
O O —_0
—
—_ Useful data: pair— — 1.23 kg/m3 pm: 1. 8 X 10'5 Ns/m2
pwater— — 1000 kg/m3 l’l’water— — L] X 10 3 Ns/m2 Page 1 of 7 1) Indicate whether the statement is True or False. (10 marks) b) d) g) h) j) The Reynolds number is a measure of the relative importance of inertial and
viscous forces. The speed of sound is higher in summer than in winter. In a converging duct, an incompressible ﬂuid will be accelerated more than a
compressible ﬂuid. For an irrotational ﬂow that is steady and incompressible, the Bernoulli
equation applies between any two points in the ﬂow. The Mach number is an example of a dimensionless number. Sound waves are very small amplitude pressure pulses that travel at the”speed
of sound”. The 2ml law of thermodynamics does not apply in a shock wave. The average velocity of water ﬂowing in a pipe will increase by a factor of 4
if the pipe diameter decreases by a factor of 2. the Froude number is a measure of the relative importance of pressure and
gravitational forces. The speed at which a tsunami travels depends on the depth of the water. Page 2 of 7 2) Starting with the momentum of a ﬂuid particle entering a control volume along a streamline
and the momentum of a ﬂuid particle leaving the control volume, derive the following
expression which relates changes in momentum to the sum of all external forces acting on a ﬂuid element: mf(‘72 _ ‘71): FE (10 marks) St a " ‘
.  u‘ —U"
Page30f7 __ F; .. WEEK 2.. ‘) 3) Water at a pressure of pgage = 10 kPa, ﬂows in a horizontal pipe, which has a 180° bend as
shown in the ﬁgure. Given q1 = 10 m/s, and a constant crosssectional area A = 0.01 m2, what
force must be applied by the clamps to hold the bend in place. (7 marks) A = constonT ﬁlm‘tys  ﬁPMM‘ — 17E = Q?l\ﬁ+ ZS? PM. f = Z (@000) (0.0%: 1— 2. (torso) (ltdL (OJ9‘»: A = 2.100li E. Dalc: “(cmAlums {0 +1“ 34%me ﬁuakm‘ H1 'PTCMLLft
mu he ml and: +quﬁwu4 H“ Clam. Page 4 of 7 4) The energy equation for adiabatic, frictionless, steady ﬂow is given by: & Lie
ds— p2 ds _
Show that for an ideal gas, where p = pRT and e = C VT, this equation leads to the relation:
p:C1p7
(6marks)
d o «it?  9.? is.
6': Q'T '= Q”: #7 f = S d5 :2. 5
5\
E: if _£C:? £)é_§ :0
SI d5 g R 52 5
ii? ._ Q .L + _?_~_ {5
? d5. S Q03 $
,_ l n+2) his
Qv § CLS
,. H5
5 M
\X l y In Jr COM—1+
let(grep V3 W? " S Page 5 of 7 5) Given the unsteady, twodimensional, incompressible ﬂow ﬁeld: mar) = 2xy(l + at)? + (ax2 + by2)(1+ et + ftz )j'
Choose the constants a, b, e and f so that (i) the equation of continuity is satisﬁed, and (ii) the
ﬂow is irrotational, that is, has vorticity V x \7 = 0. Find the scalar potential ¢, such that 9: V¢.
(7marks)
UL: Zx‘SlHokk) u =(ax‘+le~11)ll+e.¥ + 5H?)
at v
g; = lwlwc) 173' 7.51 hut +t;+f)
Com‘x'tkmh'g. :.~%§ :0 =7 ‘3: '1 u : (Ont1ws1‘) (Hurt)
Q: 0
3—“ = ZAL‘+H~5\ AU‘ _ “Znx Ll+$£)
‘8 "5.1 ‘ FM 9’ 5+. am: 9:; . u “ix—KUWQ _) 9f: lleHMc) + Oklalit) um 25’ 3 tr : ;EUUM) ._.> 9’= (M— a )llHQ + Cilia)
+1
94. (,szs 3“ mt) + 030,) Page 6 of 7 6) A viscous liquid of constant pand ,u falls due to gravity between two inﬁnite plates a distance
2h apart. The ﬂow is fully developed, with a single velocity component in the zdirection, v = w(x)k. Find the velocity proﬁle between the plates. Assume atmospheric pressure
everywhere. (10 marks) 2h 4x.
lv[X] "C‘ X £1: Kora
Z
Lx In stead: MW, Hm Dual ”faAkita w‘\\\ m be welaalrté.
4’le €51»?in «FL £91m: balance: at? 3151  ”L $23.8 — $3 51%;“; =0
(Dcm aux z 493 smite: Qt
_._._£‘ AT.
3 3 ,7) ___...— :33 L
“QM3W0». Fluital. °C=jx§§ 1..) #933; 7.3% lli'ﬂtiroAKNS: Q.“ a! EL+Q .3 W‘ ﬂxliQ‘x‘lCZ 41:. ,u. ‘ Z,» _ k1
BowmAaWi C S! L“ [k\ =0 : 53 lb; * CJ‘J‘ CL=O C?" lg “3—13". 19" Page 7 of 7 ...
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 Fall '08
 O.Trass
 Fluid Mechanics

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