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# set4-answers - 3.3 An incompressible fluid with density p...

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Unformatted text preview: 3.3 An incompressible fluid with density p flows steadily , past the abject shown in Video V3.3 and Fig. P33. The ﬂuid ‘ Dividing velocity along the horizontal dividing streamline streamline (—00 s x S —a) is found to be V = V0(l + a/x), where a is the radius of curvature of the front of the object and V0 is the m,» upstream velocity. (a) Determine'the pressure gradient along Po (0) this streamline. (b) If the upstream pressure is p0, integrate the pressure gradient to obtain the pressure p(x) for —°° < x S "-a (c) Show from the result of part (b) that the pressure at the stag- nation point): (x = -a) is [20+ pVﬁ/ ’,2 as expected from the Bernouﬂiequanon Stagnation point I FIGURE P3.3 (a) ﬂare/5g where v==v,(M—%) ThusJ #:gybi/ﬂ— it %:—€WI+& Met Ffavztx'ﬂx ”‘l x (b) [din =f§l§dx = pal/2f (3": ‘L “git/X Nofe‘f-‘fg alt/twee fa X“°’ -00 OI“ 2- a x f'ﬂe‘Pal/a [-76 ”6’7?- (C) From qufﬂ’); when X=va 70! =ﬂv’4l42l'a'" 274‘“ 2% 29%2 x=-a " From Me Bernoulli equafion ﬂ, + 2 (0V 2"; f, +35 where ’ l I“ Vo (I +010)" 0 ~ v — v 77th a: @1914“ 45 expected XV“ swa, 3.1”! Water in a container and air in a tornado ﬂow in hor- izontal circular streamlines of radius r and speed V as shown in Video V3.2 and Fig. P3.lZ.Determine the radial pressure gradient, ap/ar, needed for the following situations: (a) The ﬂuid is water with r = 3 in. and V = 0.8 ft/s. (b) The ﬂuid is air with r = 300 ft and V = 200 tnph. I FIGURE P3.12 Far carved, dream/Mes, .. 59 = ﬂz+ygs , or wizl/J \$50 (humid/vial sfream/I‘Iyes)J 7? ’7 ﬂ and ﬂ = " %: .i/I/s becomes - V2 2% — er , 5:) WW) r = 7% H and V= 0.8—?! and Wafer ((3:57? %), . / f 1 \$48 s—L——"“‘ Sir—(0.3;) == 4.97 +39; = 4,97 {5; ' - 883.? ﬂ “ (b) Wnlh‘r=300H and V: morn/2460”], j: 293 5 and air ( 9:0000238 \$5), , 3-40 3.16 A 100 ft/s jet of air ﬂows past a ball as shown' 111 Video V3.1 and Fig. P3 115 When the ball is not centered / ia the jet the air velocity' 15 greater on the side of the bail near the jet center [point (1)]tt1ari it is on the other side of V1= 11° "/5 the ball [point (2)]. Determine the pressure difference, [22— p1, across the ball if V, = 140st and V; = 110 ft/s. Neglect gravity and viscous effects. V, = 140 ms V: 100 ”/5 (’2‘) The Bernoulli equation from ~ 1. point‘ (3)1‘0 (2.) and (4) {o (/) W'ﬂ, l FIGURE P3.16 grail/7y neglected git/es 903 2L2=€V3 fz'l'zpvz and ﬂint-2L“; ”ﬂw‘éeli" 80" £3: f4!“ 0 dﬂa’ié—‘T V 77703 eye” szlmugﬁ pain/5 (I) anal (2) are ”of 0/7 71/73 SW”? dream/ME, f), + if) =23 +4 9142 0/“ 2. 2 {Jr/é ._. i904“- m g 2L(o.00238§-£T”§£)[(l40§t) —(uo #1 ] 5/03 lb _—_ 8.9’3 W315; = 893 ﬁ— 343 Baa—"W 3.32 Water flows through the pipe contraction shown in Fig. 133.32. For tho given 0.2-m difference in the manometer level, determine the flowrate as a functiouof the diameter of the small pipe, D. IFIGURE P332 1"- +14. +z,=1%=+y£ +2z lube/Pei Z,=Z;, Mall/2‘0 7%de V" _ 7. 4‘ +7.; - 1% Buf ész and 1:0,2m+)( no vl/Im‘. V,=1lz;(o.zm)(2/?3£vgzr)(02m))‘l/“= ,73 m 3—. Q3414 12mm) (mm-700156 fora/770 —___.._ —_,_.—_. Closed and water barometer indicates a reading of 30.2 ft. Determine the maximum value of I: allowed without cavitation occurring. Note that the pressure of the vapor in the closed end of the barometer equals the vapor pressure. 3-in. diameter 3.39 Water is siphoned from the tank shown in Fig. P339. The 1‘ - S'in. diameter IFIGLJRE P3.39 , __ s v , - - £9 + 2; 1+2: £+ ug-i—Zz where f}, '0, W '0, f2 ‘ﬂmpar 77m, > , Z! ‘0’ Z?- “ H (”1229“ 22+? +6H [2112‘ ’00 +30.2H r 9.7), or s/ﬂm ﬂgﬂrapar, ﬂy; 0» :_30‘2 ﬂ £78055 1 z 0— —— ~3a2 ff +1}; +5191 w" E?— : 26‘.sz or- lfz=[2(32-2§£>(7—%1ﬂﬂ 73w, - f [(1 ~ 39.55;. Since lé/qu'vzﬂzj Ié=-,73—2—-32lé~*s,». or .. f‘ \é— Hez “575 Him/aver) 0 . ﬁrl+zlgz+a=é+v 2; 0" ’6'42‘04/7 770: Hz '2’ 1/2 (3.22::— ﬁNi H or ii: 3.13 26‘ 3-36 3.50 Water is pumped from a lake through an 8-in. pipe at a rate of 10 fta/s. If viscous effects are negligible, what is the pres- sure in the suction pipe (the pipe between the lake and the pump) at an elevation 6 ft above the lake? 401 it 1/2-..Q_‘_462 ___j‘_(/05) ‘28.6ﬁ ,92 774.2. 77 £1992 . .5 Tim, 12. f2 ..-_— -372 "%PV22 = ~62.¢;F% (6.0 ff) —%(/,7¢ 21%;) (29,5?)2 IA 3-y7 ...
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set4-answers - 3.3 An incompressible fluid with density p...

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