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set1-answers - L"? Determine the dimensions of the...

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Unformatted text preview: L"? Determine the dimensions of the coef- ficients A and B which appear in the dimen- sionally homogeneous equation dlx dx W+Adt+Bx—0 where .x’ is a length and I is time. 7 dt1 4* {1.7"} m 7'3 + mm -= o Since Cac/p ‘l'erm musf have fie same dimemfms: [A] [LT'] :3 [1.7"] 5-I1m‘ __ 0V mmmmm - I 1.10 i'l‘he pressure difference, Ap, across a I I-cdsitthL'ZT), p the blood density (ML‘3), D“ ' partial blockage in an artery (called asteriosis) is the artery diameter, A0 the area of the unolb- approximated by the equation structed artery. and Al the area of the stenosis. #V AU 2 Determine the dimensions of the constants KL, 3P = Kr “5 + K“ — 1) PW and K“. Would this equation be valid in any sys— tern of units? where V is the blood velocity, ,u the blood Vis— 2. 1/ [£0 .. t] V A P = k V A95— + k“ A. f m M [till—Hm] «italif ‘53 l Elli-l" Since each term mast have five same dime/45mg, My and K“ are d/Jrnensi'm/ess, 774145, We 63mm” 1': a 7enem/ hamzoyewoas quail-[on 474% Moa/c/Le va/ic/ m my flows/skml sysk’m 075 emit-5. es. 1.51 The viscosity of a fluid plays a very important role in determining how a fluid flows. (See Video V1.1.) The value of the viscosity depends not only on the specific fluid but also on the fluid temperature. Some experiments show that when a liquid, under the action of a constant driving pressure, is forced with a low velocity, V, through a small horizontal tube, the velocity is given by the equation V = K/p. In this equation K is a constant for a given tube and pressure, and y is the dynamic viscosity. For a particular liquid of interest, the viscosity is given by Andrade’s equation (Eq. 1.11) with D = :5 X 10'7 lb - s/ft2 and B = 4000 °R. By what percentage will the velocity increase as the liquid temperature is increased from 40 "F to 100 °F? Assume all other factors remain constant. V ° "' Vq. ? ' = ’1: Increase in V = I ’,°° ° actor: and £10m Eismdcz) ‘ %‘—i}:wo = .... xléo K/Iu‘io' "/0 Increase in V =- R‘fim Andmde’: eguaein'w a” z ‘7 : (‘la’F-i‘féo) . /U'fo° ' 5x10 8 if . 000 and /(/1 .7" 'Efll'D-qe (loo‘F-f‘fw) l 0‘ Thus I, From 5%, (31' « _., boo , 5X“) e 5'00 “'tncras‘e m V "=“ _ i 0,, [5 e 5xlb7e, sea = 13421. As shown in Video V1.2, the “no slip" condition means that a fluid “sticks” to a solid surface. This is true for both fixed and moving Surfaces. Let two layers of fluid be dragged along by the motion of an upper plate as Shown in Fig. P154. The bottom plate is stationary. The top fluid puts a shear stint bit the upset slate, and ma lower fluid puts a than was on the bottom plate. Determine the ratio of these two shear stresses. ' ‘ ' Fluid 1- Fiuid 2 H2 mls+| I FIGURE P1.54 a a (may; to,» Surface: Far «clMidL : M5 2. ZOE 7; ‘-‘ A ('33 )aam and” W m M) = M” Thus ’ fl _ , _ (who? sump“: = 20 %z :- 1 TL?on swim. L0 £1 1-; /— w, 15‘! A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. H.517. Determine the magnitude and dhrec~ tion of the shearing stress that the water exerts on the fixed surface for U = 2 m/s and h = 0.1 m. T—‘fl '7" FIGURE P153 77mg.J ai- '/’he #Ikec/ surfiace (31:0) 43 7:0 «5 50 771472‘ 3 {2 lm) TA'fl = é/JX/ow (‘21:) _—_- 9:, 943? x “3-2 J! «cf/:77 fl; d/recfm” all f/aw 1 155/ logy 1.84 As shown in Video V1.5, surface tension forces can be strong enough to allow a double-edge steel razor blade to “float” on water, but a single—edge blade will sink. Assume that the surface tension forces act at an angle 6 rel- ative to the water surface as shown in Fig. P134. (3) The mass of the doubleedge blade is 0.64 X 10’3kg, and the total length of its sides is 206 mm. Determine the value of 9 required to maintain equilibrium between the blade weight and the resultant surface tension force. (b) The mass of'the ‘ F i G U R E 91 ' 3t} single-edge blade is 2.61 X 10"3kg, and the total length of its sides is 154 mm. Explain why this blade sinks. Support your answer with the necessary calculations. Surface tension force ' (a) Z Fuevltal :0 {LU : TSl'n 9 where v = mnHadex' g Cmd T: (T‘x Jemfl‘h 0% Sides. (OW KID-3&3) (ml Mtge): (73L; “7%){0 20L m) sine StnB‘ 3‘ o-Ll’5 Q}: 2,45" (E) For SIny/e~ed3e blade ‘3 2d :Mbladex 2 (2.4:! KID I‘M/52’) :: 0.025!» N Ctl’ld T sine = [Tx leng'lla mil/ml me = (7,3W,0«2 N/fm){0./5H‘/m) 5m 9 : 0.01:3 5M9 In order acor blade “xi-o "qt/oat” %< Time. Since Maximum: Value acoY‘ 5M9 15 l} H” ‘icollows "but %>Tsm9 4nd 5in5/c-edge blade will sink, ...
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set1-answers - L&amp;quot;? Determine the dimensions of the...

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