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Unformatted text preview: PGE 322K — TRANSPORT PHENOMENA
Spring 2008
EXAM 1
February 26, 2008
Except where noted, do all calculations in SI units
BEWARE OF UNNECESSARY INFORMATION.
DO NOT SPEND TOO LONG ON ANY ONE PROBLEM.
DO NOT LEAVE ANY PROBLEM BLANK!
YOU CAN START ANWERS FROM EQUATIONS IN BSL, JUST GIVE THE
EQUATION NUMBER
Total:100 pts NAME Spring 2008 l) (20 pts) You are pumping a ﬂuid through a cylindrical tube with a head difference
of AH and measure the volumetric ﬂow rate exiting the tube of Q. You then
double the head difference (to 2 AH), but ﬁnd that the ﬂow rate increased by less
than a factor of two. What are the possible reasons for this observation? Circle either P (possible) or NP (not possible) for each possibility; there may be more than one possibility. Make your marks clear; ambiguous marks will be considered wrong. .
It is a Bingham plastic ﬂuid undergoing laminar ﬂow. P ® a.
b. It is a shear thinning powerlaw ﬂuid undergoing laminar ﬂow. P
It is a shear thickening powerlaw ﬂuid undergoing laminar ﬂow®N P 9.0 It is a Newtonian ﬂuid undergoing laminar ﬂow. P NP
e. It is a Newtonian ﬂuid undergoing turbulent ﬂoNP Spring 2008 0.002 In £7 , 2) (40 pts) A Newtonian oil is driven through a 0.002m slit (xdirection) of 1 m length
(zdirection) and 0.1 m Width (ydirection) long. The head difference at the two ends is
2.4 x 103 Pa (the ﬂow is in the positive z—direction), the density is 900 kg/m3, and the
viscosity is 10'2 Pa 5. You can assume the ﬂow is laminar. a) Sketch the velocity proﬁle VZ(X) on the ﬁgure above. b) Calculate the maximum velocity for this proﬁle. QQFL A sLn’ USL } ~ L .— mwomm V; W, L“. o WW» 9~°° *5 “6 9x»?— QLHON 09 NC, 5UT3
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‘ LC\©’1 9M5» f l.’L X \o'1 “Is Spring 2008 0) Calculate the total ﬂow rate through the slit. 5K\T < > % V1IM’, :' 2XQﬁ1 a 1 ll!) W {V}? : L'W’wa K‘\u¢1 H‘ '8 ‘XLQ’IH/s
QL d) Now an inﬁnitesimal thin sheet of metal is placed in the center of the slit, as can
be seen in the ﬁgure above. Please sketch the new velocity proﬁle vz(x) on the ﬁgure. e) Calculate the maximum velocity for this system. r— x 'W
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t: ’5 mo “V5 Spring 2008 f) Calculate the TOTAL ﬂow rate in this new system. 1
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3 3° ‘1 "lXio'g MTV5 f) Now the center plate is pulled in the positive zdirection with velocity V. You
can externally control this velocity V, and you wish to set it such that the total ﬂow rate
in the new system (with interior plate moving a velocity V) equals the total ﬂow rate in
the original system (no plate). Find this velocity V. (Hint: if you understand the physics, you can solve this problem without doing anymore math). \@ V1VQHW («Ht (21m is) \(od ” VELOCITY Qnﬂ’v b
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P = 2.0 x10“ Pa The two cylindrical sealed tanks are partially ﬁlled with oil of density of 800 kg/m3 and
viscosity of 2x10'3 Pa 3. The pressure in the gas regions of the tanks are as given, as well
as the dimensions of the tanks, and the lengths of the 0.006 diameter cylindrical tube
connecting the tanks. You can use g=10 m/s2 for simplicity. a) Calculate the total head gradient (AH/L) along the tube between tank 1 (left hand side)
and tank 2 (right hand side). Which direction will the ﬂow be in? LET %90 AT QONT P, Tug/fl ‘1 P + l} " LSYWV‘ pa,+(200k‘6/m3)k\0k/31)(0‘7Q
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Spring 2008 :— 3» q Y ‘ 0 ?(LO‘“\ wkdké’k To rrlhq'ﬂ’l.‘ 10 b) Assuming steady state ﬂow, calculate the pressure at point P. Twﬁ TUISL CONHEQ’YHJL ma (#NKS "\5 Op LOASﬁA‘h’T moms. Sink?" "T‘kF, ELOU Me New M; (OASTQNT Meow ’n—us TU$C3 v' {COMyE’m/Prﬁo” “9 M“) LH Nut”? (56, coesfaﬂ’e
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«rues H (@9 (30m)? «A: H (1%“ TD" "Elfl Lt? (Sp/4119944 Irwk j, 4' (PoeWP Spring 2008 mummemewm.wwmwmmwmwmwammx 4) (20 pts) You have a pipe that is carrying Newtonian oil in a pipeline. The pipeline has a constant head across of it of AH. Your coworker suggests adding heating elements to the pipe to heat up the oil.
a) Would heating up the oil increase, decrease or have no change in the oil’s Viscosity? Express your reasoning. om ts I) memo so 4* \L_ﬂ 3
(Yoke, V\bLQS tTV/ u i\\. be CMSQ. b) For the rest of the problem, assume that all the only property of the oil that can
be affected by the temperature is the viscosity (i.e. no density changes). If the ﬂow was
laminar, would the ﬂow rate of oil be higher, lower or the same for the hot oil compared to the cold oil? Express your reasoning. smite 4%; ‘v‘tbtobm w»; oammsm we Spring 2008 c) If instead, the ﬂow was highly turbulent (Re > 107), would the ﬂow rate of oil be higher, lower or the same for the hot oil compared to the cold oil? Express your reasoning. 'éok menu; Tofkbonﬁm Rom é(L\L:Y\oN E Acroft 6&0 9°“ “3‘0; .6, \5 A LoAﬁv’wT {Mb «we Av) 9mg A mm “QT Lamas, mum vxbwswy («qu (LATE. \5 TWP, game” d) If instead of a liquid oil, assume we had a gas. Would heating up the gas increase or decrease the Viscosity of the gas? Express your reasoning.
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 Spring '08
 dicarlo
 Fluid Dynamics, NonNewtonian fluid, Laminar

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