midterm1_solution - PGE 322K — TRANSPORT PHENOMENA Spring...

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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 power-law fluid undergoing laminar flow. P It is a shear thickening power-law 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 (x-direction) of 1 m length (z-direction) and 0.1 m Width (y-direction) 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 1;) (5—, Hi0" M , ’L {3.4%on 963 \\¥\03m\ V - ’1- NT" " ‘ LC\©’1 9M5» f- l.’L X \o'1 “Is Spring 2008 0) Calculate the total flow rate through the slit. 5K\T < > % V1IM’, :' 2X|Qfi1 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 (5A5ngka Tk-U) V) ’W‘3 5"“3 ““H (5"5YW M '1 t: ’5 mo “V5 Spring 2008 f) Calculate the TOTAL flow rate in this new system. -1 %‘ {V1,}: 1,7,) V‘emmc" hue “V3 Q: lflllgw <V7‘7\) 1‘ lk\0’~?~\)(l0’¢h\(LXtSIK/5) :7 THO &\’\“\ . 3 3° ‘1 "lXio'g MTV5 f) Now the center plate is pulled in the positive z-direction 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 r we, “we. America T‘Ns THE— 3 Spring 2008 a. l. p gv 3) (20 pts) P= 1.5x10‘ Pa 0.5 m 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 1 t ("‘3’ u - 7 q 9 "TO’TM— 1‘06 5 3.0(300 (v Umiuamo mama; AH 1 Act my PM L0kw$l PW (3e. 1. 0 Jr- (u. 00 O O T. 6% \ 3 as \/ A / O I. a \./ f‘ 0 0 (A \/ 3 Spring 2008 :— 3» q Y ‘ 0 ?(LO‘“\ wkdké’k To rrlhq'fl’l.‘ 10 b) Assuming steady state flow, calculate the pressure at point P. Twfi TUISL CONHEQ’YHJL ma (#NKS "\5 Op LOASfiA‘h’T moms. Sink?" "T‘kF, ELOU Me New M; (OASTQNT Meow ’n—us TU$C3 v' {COMyE’m/Prfio” “9 M“) LH Nut”? (56, coesfafl’e 7 I. «rues H (@9 (30m)? «A: H (1%“ TD" "El-fl 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 co-worker 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 Lo-Afiv’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. POIL Pr CJAS LuouflL T VtaLos wme /LL° TRE wbtos «'17 ukkk. ‘ /'_________/ Spring 2008 E E z E E E g t g E g g l g l l 5 5 l wesn’mwmm’ruwmmwwmwm‘a H r i n w w ...
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This note was uploaded on 03/31/2008 for the course PGE 322K taught by Professor Dicarlo during the Spring '08 term at University of Texas at Austin.

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midterm1_solution - PGE 322K — TRANSPORT PHENOMENA Spring...

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