hmwk 8 solutions

hmwk 8 solutions - E] “:0 inc) 2:15 / ’U‘Qro 57?: CW...

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Unformatted text preview: E] “:0 inc) 2:15 / ’U‘Qro 57?: CW Eb \ “a :LH— 77 E: vii/3‘: / r akflfi “’ CMVLJ :Q m 5H2”) 1am i d7; 5})” baggie: rflg:fl,rq C / r a + A) a - * (up-:3. Cl)” 3; Ci? a/L “7 'a +09%” +63 godnclcary Céh’wcflInL/DLS 1);:0 J“: R V / V/+Aere-Fore. ‘_fi 9% Q3:O $7.3):— +63 w .U—iLZO dirt/Q arékaxjté C23 :‘Q/gafl 6.3] Two immiscible, incompressible, viscous fluids having the. same densities but different \"is~ cosities are contained between two infinite, hor- izontal, parallel plates (Fig. 136.81 . The bottom :plate is fixed and the upper plate moves with a constant veloeity U. Determine the velocity at the interface. Expreés your-enmitei' in terms of U, and 111;. The motion of the fluid is caused entir 1y by the movement of the upper plate; thatis, th re , , . r . -w. is no pressure gradient in the x direction. The FIGURE P53 :— fluid velocity and shearing stress is continuous u across the interface between the two fluids. Ils- sume laminar flow. _ __ ! Ear 777: spec/fiéd Cram/1.795431) v20) oer-=0) g5 :01 and 99‘ =0, so flint file x- mmpanmi- ofl 7'71: Wafer-Stokes fgaafifius (Eg.é.lz74) «(or £1771” 77:: upper at; Ava/er layer reduces 15° Inkyméim (Mr 53. (I) glib/Cir LL —'-' (4- g 1‘" W}! [.611 75:18: 77!: 1/8/06”? magma, n: effiwr laghlr, I): The upper /47€r af- i=24“ a: 'U' .50 Want 5, —_- y. M211) - where 171? suéscnlpe I rewer 1‘9 ‘fire UFJWEV layer, F5? The lower layer 1; -0 “=9 .55 1M1! i J Bl =la where 771a subscript z ireéw 41: 7712 lower layer. Thus, Lil -:-.. A: 5129.58 777: Velamlfn, cl:.s¥rsz%z$réa 1.3 brim» I}: 84:11 lat/er 7‘11: «shear-.1317 chair 7am“ ( = 15 Mud-mi Wrouykoaf feed! layer, FE»- flie uypcr layu— : "/4, and 7/0? 73m. lower lg??? A: 42': 7511: 122;”:416; 2':le 5a 77nd: 1' I ,u, ,4, =g/«L A; or it, = if. A; A“: ! , . Sués-[1'75u2‘réy of £313)! méo Eggzy weld; .~ —i 1 _U ,42 {’42, A: + 1% UAR. 4"": 1+ WW», 777115J V'é'lacf-f-y a?!” 771: [xiii-Ferfiue. :3 U2 (5:12)} 42% = D % N f ,0 f :O {i ‘ 3+, 29 3% "O a? J; :0 3% 0 00H:- . 7.2“ A cylinder with a diameter, D, floats upright in a liquid Cylinder as shown in Fig. 137.20. When the cylinder is displaced slightly 3-" . diama'e' = 9 along its vertical axis it will osnillate about its equilibrium pu— ' sitiun with a frequency. «1. Assume that this frequency is a fune- tion of the diameter. D. the mess of the cylinder, in. and the Specific weight, )1. of the liquid. Determine, with the aid of dimensional analysis. how the frequency is related to these var- iables. If the mass of the cylinder were increased, would the frequency increase or decrease? CL) = UK (0} "ll"; . _, 2 _3 luil‘rFlGUFlE maze (or: T“ rm: F1. T (3': FL ,, E,l~3_: I Pf Hrm Vegan-rent 5’9 WT" Cheek £451.11; (ill-T: ) flym'; (I: M iy’L‘W‘" .ZOK D 6' u (1.) mar": Shire 771m :3 only i Pr‘ RPM, r'i‘ Fallows 71mi- wkere C is a. washed. Th“) ‘ 3' a): CD 3 From 7511'; rem/11' ['1‘ All”)! 7715?} if, [m 13 {IncréQSed w MN decrease. 7.3 ‘l- The drag characteristics of a torpedo are to be studied in a water tunnel using a 1:5 scale model. The tunnel operates with freshwater at 20 "C, whereas the prototype torpedo is to be used in seawater m 15.6 “C. To correctly simulate tho bc- ' havior of the prototype moving with a velocity of 30 m/s. what velocity is required in the water tunnel? E»- a’yna/m'o Jlbri/qu'r‘gl 7772 fawn/J5 nambt’r magi fie file Same kw Made/ am! PMfoing. 771nmJ VWDM _ Kg 74,, 7/ _.74;n2 Vm‘v—z‘eny 5mm) 74, {marergaam'c}: Aooyx/o""m‘/5 (EL/c 1522)) 7/ (Jami-Pr @ I542?) .= /./7x/o“"m% (7mg 2.2.), m2 D/pm25/ it Aug»: 77,6175 -4 2. _ Known» %") .. - 5 £1” :/_ch fl % {Anxm‘égi} (Jams) 5 7.56 The drag characteristics foria newly de— signed automobile having a maximum character— istic length of 20 ft are to be determihed through a model study. The characteristics at both low speed (approximately 20 mph) and high speed (90 mph) are of interest. For a series of projected model tests an unpressurized wind tunnel that will accommodate a model with a maximum charac- teristic length of 4 ft is to be used. Determine the range of air velocities that would be required for the wind tunnel if Reynolds numberisimilarity is desired. Are the velocities suitable? Explain. 5r Regan/d5 numéw Jimflen'fi, :1 1:? / flan. fl?“ wéi—“fifit 51m: 777: tum}! 71mm! :3 unprlvmiwy'wl 77m 4:}— ,Dropmlt'es will be approx/Mam; fire some 7‘54 Model mdpm‘mfype. 77mg 53,0; flex/«ca: 7‘9 Wm = 4a; 4mg fir #16 (142$; fix/(M _..: (20795) = V4” MALJV mffilérf) m! flow speed £%=5éme=MMwh and 07‘- fllgh speed I %:5 (ygwpt) = 6‘50 rmph do Writ 7718 made! Velacf‘l‘y #47429 /.5 ADD mp}: 7L0 stramph , H fie firék 1/2/9617? H} We Mild 7Lu/me/ empressflw'h‘vig of 77!: air (rt/014161. start 7’0 bt’L'amei 4w Iiwparfrfaf 79(7er wherms Coumss/h/fl‘? 1.? be?! .Ib‘ipclrffiwé 76;» 771a pmzlfigpe- 7551.; 777a higher Lie/95H? Vega/MM 5751’ fire model luau/d not be 5uz+4L/e, Il/a. So filfié 17~¢3 7.57 If the unpresgufi'z'e'dmwind tunnel of: Problem 7.55 were replaced with Ta tunnel in which the air can be pressurized isq‘thermally to'_ 8 atm (abs), what range of air velocities would; be required to maintain Reynolds dumber simi—é larity for the same prototype veloc'ties given in! Problem 7.5L? For the pressurize tunnel the maximum characteristic model lengt that can be accommodated is 2 ft, whereas I 6 maximum characteristic prototype length remains at 20 fr. 5r Pagan/d5 number" wind/write J A1,, w“ = AV} M‘“ /"’"‘ ‘ ISO 1114* l %%%fiv M F!»- m m7”! 345 J 7554/87"? , 421d oér Kramer/21d wmpresr/a'n 7? —'= 601115 flint 771145J 4, ‘ __"":. = _. Ion" (0 U/aere it! 1:: aémpspber/L pressure (Pressure «1‘ Mae}: prefer pe D/qorpks )J and 73" I; fmssqre of Ganymssar/ 4/)- zh #16 MM. flfl€/. l For 1353/: _ ‘ t) h _ I41— (%J%% v- 1-25 V 7M5) ai‘ bu) rifled - L4,, = /. 2? {20mph} r‘ 25%?” and «7‘ high speed ' V4" = £25- 479,”pr = //2.5‘4nph 7716119 £213 771: mega/fed mede/ w/«hfy Fringe 1.3 JS'M/J/z 7‘9 1/2.:Trmp/7'. ...
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This note was uploaded on 05/04/2008 for the course MMAE 310 taught by Professor Wark during the Spring '06 term at Illinois Tech.

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hmwk 8 solutions - E] “:0 inc) 2:15 / ’U‘Qro 57?: CW...

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