set11-answers - 7 3 LI The drag characteristics of a...

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Unformatted text preview: 7. 3 LI- The drag characteristics of a torpedlo 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 at 15.6 °C. To correctly simulate the be- havior of the prototype moving with a velocity of 30 m/s, what velocity is required in the water tunnel? F29;— dynamic, 61m; /4r/ 7’3 #72 fawn/d3 numbfr musf be 725 Same for Mode/ and ,Dr‘az‘oigpe 771015 Va»: DM .= Z9 m, p 7/ 60 Wet _ V»: .2 km“ a: em V 5/1466. [email protected]’C)-= [00¢ nib/my; [TA/e 132) 7/ (Sea/«12w (CD/5&1): //7x/o 6414/ (pa/e /A) 4/25! 9/12 :5 it 74mm 7m 4, V: f/aMx/D 34') (5 —”-" =/z7fl ”’4 (//7xw“ 41") N905) 5 7-91 7. 43 Water flowing under the obstacle shown 111 Fig P7. 43 puts a vertical force, Fv, on the obstacle This force 15 as$umedl to be a function of the flowrate Q, the density of the water, p, the accel- eration of gravity, g, and a length, 6, that characterizes the size of the obstacle. A 1/20 scale model 18 to be used to predict the ver~ tical force on the prototype. (3) Perform a dimensional analysis for this problem ('3) If the prototype flowrate IS 1000 ft3/s, deter- mine the water flowrate for the model if the flows are to be sim~ 11211. (c) If the model force' is measured as (Fv)m = 20 lb predict the corresponding force on the prototype. (a) Fv=f(6?,flng/Q) _ (0 1:2: 1W .091", :1 C9 Thu; 11/5771 50:; acts 0.557“; (C) 7716 Precltcl'mn 93144.50” Ls Fix 1% ”£31 131 £35,». “I; So ’hmi F}, :3 F 49 2' I (0 :1“ FL- From 77% P6 The» rem} .513 2 fig J-t’rm: regwrepl an d d; dimenJ/ona/ firmly»; 51e/d4r IFIGURE P7.43 “-2 ‘{547' 15L (1,) For JJm,'/ar;+, 111W“ mac/cl am! 1311543,“; 1 WW1 WW(~1%) ”31ft? The drag, ‘22), on a sphere located in a pipe through which a fluid is flowing is to be determined experimentally (see Fig. P750). Assume that the drag is a function of the sphere diameter, d, the pipe diameter, D, the fluid velocity, V, and the fluid density, p. (a) What dimensionless parameters Would you use for this problem? (b) Some experiments using Water indi- cate that for d = 0.2 in., D = 0.5 in., and V = 2 ft/sj, the drag is LS X 10‘3 lb. If possible, estimate the drag on a sphere located in a 2—ft—diameter pipe through which water is flowing with a velocity of 6 ft/s. The sphere diameter is such that ge— ometric similarity is maintained. If it is not possible, explain why not. (a) 08:76 [91,0] Vl/o) '95": 45:1 13:1 1/:‘LT" fl: Ill-“7'2 Fifam We ff flew/em, 5-3 : 2 pi vhf/rim raga/Md, and a. dimenfix'amr/ 4/44/7513 9/22/49 ”it we) (A) The Shin/”[717 regal/Emmi A} at” a! _—-—— 0,“ mo 5" ”Vi 0.21;}. _.__ d 446) age/n. 2 +2- and A: 0. 3 74:5 (raga/it’d 074ml”). Thus, 7716 PY€JIC51L1031 geium/z/aiv LI: ,8 g .29 ,‘ 444 M201 xii/4:04: Wind blowing past a flag causes it to “flutter in the breeze.” The frequency of this fluttering, w, is assumed to be a function of the wind speed, V, the air density, p, the acceler— ation of gravity, 3, the length of the flag, 6, and the “area den— sity,” pA, (with dimensions of ML”) of the flag material. It is desired to predict the flutter frequency of a large 6 = 40 ft flag in a V = 30 ft/s wind. To do this a model flag with 6 = 4 ft is to be tested in a wind tunnel. (a) Determine the required area density of the model flag material if the large flag has pA = O 006 slugs/ft? (b) What wind tunnel velocity 1s required for testing the model? (c) If the model flag flutters at 6 Hz, predict the frequency for the large flag. ‘ w=£(l/Jipi?i’e2fl4) 40:57", ViLTUlf’fML‘? g5/v7-‘z fléL fii/‘(L-Z‘ From #76 [2/ Theorem, é‘g ’L' 3 PI +€rms Vega/Val 4144 4 dimeHJIa/M/ dim/751.: 7/2/43 QJV:——= 7L(V;/—7) 7-2) (a) Fzr J/bnlar/rf ~ rfmlm 41M 5114.0: fl”: $1-]; 10/; ,0 e: ”“ [-5) gr 51m.4)aI/:/‘y 14m “V2517; 4'an win 5 :5 MW: @V = V560?)= 9.47% ct) W’h 7‘7“ similarrl‘y rézliiremé’nis 54111.56?! We Predfcéfm €Xuafino'n 15 Cu V? : f £04m V3312: 50 flfl/‘E F V—E—fiw — 7-— (96 7- &5- 7.6.5' The pressure rise, Ap, across a centrifugal pump of a given shape (see Fig. P1653) can be expressed as 8 AP = f(D. w. p, Q) where D is the impeller diameter, to the angular velocity of the " _________ impeller, p the fluid density, and Q the volume rate of flow' 6 ”WWW—imam“? mmmmmmmmm a """""""" through the pump. A model pump having a diameter of 8 in. is i ' I tested in the laboratory using water. When operated at an an- gular velocity of 4077' rad/s the model pressure rise as a function of Q is shown in Fig. P7.6§b. Use this curve to predict the pressure rise across a geometrically similar pump (prototype) for a prototype flowrate of 6 ft3/s. The prototype has a diameter of 12 in. and operates at an angular velocity of 6071' rad/s. The 2 t s prototype fluid is also water. ‘ E 2 _, ! Model data ; (um = 401: rad/s Ap=pzepr o 0.5 1.0 1.5 ' "2.0 Qm(ft3/s) I FIGURE P7.65 Centrifugal pump ~ - ,,,,, (a) AP: £{D,43/,4)> Ape/1'” 125 L A): T" g: FNT‘ Q ;- 1.37" Ham 1%: Pi 'theorrm/ 5‘3 = 2 PL £0712: ”gt/Wed, 41,14 4 d,,,',m5m'”’/ firm/gm} g; 614/5 ‘ Ag =¢LQJ . . My 771(15/ ’fhe Similar/5‘7 mil/Ikmflti IL: 4% =.Q QMDB 0D I»! _ M D 3 mm 74/ fire 44%: j/Vf/I 4”": (W $73502 #3) = mi” (W :3!) mg. P7941 7'21? jot/é (Fig, i016?!) 4,9,” 2.5750123 743V 43., ”/73" . ”ms, AP Ag, KW” 8:04:12.) fl urn: fl‘fl ( 4): 4/1 I "rm 2 r4 ‘ e 77» , /z . I t ésafpeyzsf = 41—5—— ., —-.”' ) (5750px) 13%" Wm 1%” ”" ’7‘” " 9'”- (%7? = 27.8 gsé 59772419 7".7/ 7. 47‘ i in? A viscous fluid is contained between wide, parallel plates spaced a distance it apart as shown in Fig.1 P7.67. The upper plate is fixed, and the bottom plate oscillates harmonically with a velocity amplitude U and frequency w. The differential equation for the velocity distribution between the plates is Bu - 32” p _ [‘1' ayz Fixed plate at where u is the velocity, t is time, and p and ,u. are fluid density and viscosity, respectively. Rewrite this equation in a suitable nondimensional form using h, (J, and a) as reference parameters. l a My" 1: are" & 9‘ g, if ,- 20.1f- &_‘j 33/ a3 51 IL: 5 or a: 3 flaw] W ~ 2W" ...
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