# 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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