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Unformatted text preview: 3.22. Some animals have learned to take ad vantage of the Bernoulli effect without having read a ﬂuid mechanics book. For example, a typ ical prairie dog burrow contains two entrances— ya
a flat front door, and a mounded back door as
show in Fig. P3.21.Wheu the wind blows with
velocity Va across the front door, the average
velocity across the back door is greater than Va
because of the mound. Assume the air velocity
across the back door is 1.07%. For a wind velocity FIGURE p311
of 6 m/s. what pressure diﬂ'erences, p. — p1. is generated to provide a fresh air ﬂow within the burrow? ﬂ +ﬁ (owl1L 3‘2, = f2 +épl§2+ 3’22
Thus, MM neg/@349 gram’m‘rbm/ effecfr (4219. 3:22;)
war/0:. = éeﬂ/fVF‘) = 1’ (1.2? %) (0.07“?)32 ' (6 :92) Of"
/V
f, —/92 = 3.2/ 751' 3.32 Water ﬂows through a hole in the bottom of a large, open tank with a speed of 8 ms. Determine the depth of water in the tank. V15
cous effects are negligible. 2. 2.
,p, + 2'10” +52, 702 + Z'LPI/z +d‘zz 77m; wifhﬂ=ﬁ=21=Vt=Q 2:;
0‘2, sz’vpvf I ”ﬁerce i=9; and 2,4) 30 Mat 1 (735:2?) Va. 0F 3.33 Water ﬂows from the faucet on the ﬁrst ﬂoor of the
building shown in Fig. P333 with a maximum velocity of 20
fI/s. For steady inviscid ﬂow, determine the maximum water velocity from the basement faucet and from the faucet on the
second ﬂoor (assume each ﬂoor is 12 ft tall). (SJSJ
. a).
v = 20 We hf Z
159 + _i_/__ + Z = cami‘anf ti” 2'}
V2 _ a. g:
Tﬁmj éLiﬁéfz,  %+%+Zz uni/j [1:76,ch (freeﬁ!)
W (20w 1 M I4=2Wr me
If V ___
.s f ’ + ~6’f7‘) 2 ~ 9701!
2(32.2ﬁ) + 5‘ 7’ 26.22%) ( Z 2. 2
4/761! %’+_M__ +2! g. J+ZV;_ +23 w,§jﬂ?:// :0 Cfrged'ef)
an [45.20395 3/:415’
ZJ=/6f7‘ , iéz
W32.st H‘H — 2(32413‘1) + M H or V3 =1/2o ’ .— 2(32..2) (I2) = 1/ __ 373 Impmw’é/e.’/Va f/ou/ from second! Mm faucaf. Tim The “super maker” water gun shown in Fig. P334 can
about more than 30 ft in the horizontal direction. Estimate the minimiml pressure, 13,, needed in the chamber in order to ac~
compﬁsh this. List all assumptions and show all calculations. A aggﬁmimvgﬁwﬁ . MEWS gﬁwmmﬂi P
l _ E 2
33% aw: :. Pam “L 2‘ J
. "F“ “E“??? a K} M‘ ﬁﬂfﬁﬂiw M5; . 3.38 Water ﬂows from a pressurized tank. through a 6in.diameter
pipe, exits from a 2in.diameter nozzle, and rises 20 ft above the nozzle as shown in Fig. P338. Determine the pressure in the tank if
the ﬂow is steady, frictionless, and incompressible. 1' 2
%L+2¥;+Z, = 1 +_;‘— +22)
where M50) V150) Z, :2”) EL=ZZHJ muff; :0
TIN/5, %‘ =5 22.," 2, “FIGURE P3.38 01“
f, = {(2143) :ézﬂﬁﬁXzzHﬁﬁ) = £21,400 #11 M5153: The diamefcr of fhe Mac or ”ﬁzz/e me 1701’ ”Na/96’. 5H? Water flows from the tank shown in Fig. P3.!9‘0.If viscous
effects are negligible determine the value of h in terms of H and
the speciﬁc gravity. S0. of the manometer ﬂuid. 1 _  .— ’92 ‘= J'(Hh +5612)
Combine Egm. (I) and (7) it: give:
H = (H +(sc; —/)h) or
(36—1)}; =0
77:12.5) if 36%}, Men [7 =0 {era/1256 (I) (2) 3&8 Air is drawn into a wind tunnel used for testing auto
mobiles as shown in Fig. P358. (a) Determine the manometer
reading, it, when the velocity in the test section is 60 mph. Note
that there is a lin. column of oil on the water in the manome
ter. (b) Determine the difference between the stagnation pres
sure on the front of the automobile and the pressure in the test
section. Wind tunnel I FIGURE [33.43 2.
”V
(a +2 +4 " 42
) éL ’ 1?”? i
where
2, =21 Maﬁa, and 1420 77m; was 14 s Jew/A =— ate—fl , Pz= —ept‘=——(aoozsei’—”Emﬁ) = we ll H3
By‘f fz'l‘K'zob 3;,7(Tiﬁl)=0 tubere 4:17 =0W9a20:09(62¥fﬂ%3)
This; "2562123 422145524; me—Jn (M) a (Jr/7.102232% 2 (5) [’5 +22 4—5: 1% 153+; where
22. =52; aim/V =0
77m: ﬁre42:7; =4: or ﬁgvﬂze {Pl/z ="2L(0.aaz33 %){€€§i)2= ﬁzz—7%,; 3.50 Water (assumed inviscid and incompressible) ﬂows
steadily with a Spacd of 10 ftfs from the large tank shown in Fig. 50 lb/fta
P350. Determine the depth, H. of the layer of light liquid
(speciﬁc weight = 50 lb/ft“) that covers the water in the tank. From fhﬂ Ber/701)”! €fVafiaﬂJ I Fl G U Fl E P3.50 %+E§f+zl=. +$z+zz wbem‘ 10/: J; I:J 16 =0, ”2:0, 2, = 6‘29’; 417de ”.5 {'3‘
771115, 3333.}; +z,= 72 fizz so Hm! wif/J V= IOWA" so Iii/H3 (/0 {ml/s)
62.4'lb/F43M 4‘ W1” W +5H 7773M (are)
H = an: H I"33.58 As shown in Fig. P358, water from a large reservoir ﬂows
without viscous eﬁects through a siphon of diameter D and into a
tank. It exits from a hole in the bottom of the tank as a stream of di
ameter d. The surface of the reservoir remains H above the bottom
of the tank. For steadystate conditions, the water depth in the tank. It, is constant. Plot a graph of the depth ratio W as a function of the
diameter ratio 071). .ld a F I G_U R E P358
From 11/79 Barney/5' equation;
%L+7%+z’ ‘ %+% +32.
where f; = l6 =0, 2'; ‘5’ .. W, at 7776‘ ”freed'ef”end of the “PM
f1 = m 41) . Thus; 5?, (I) became? V; v;
g“ (h‘zl)+’2'_§ +2; = h+3zif
w Vzﬁ/zymm'
ﬁ/sa, 1
€14E+th :: 3+$+Z3 Wﬁﬁ‘f‘e ﬂying/03 "Zj‘gaﬂﬂ’zﬁ‘A
1?
77m; 1
h = Me. or ﬁlm} for canrfanf lr'yuia/ IEVEIS I)? 7936 tanks, 0; :03 or
ﬂZVZ 5”} V3
so that
(so if 19le =¥41é
From 5?.(13, (2.), and (3) *‘ NW =d‘W or H =(%)"‘h Th Us)
.3. —. W 7M: raw/7‘ f: p/oﬂed M 11/29 179le [0499* (can ’7‘) hIH ("D 3.5? A smooth plastic, 10m—long garden hose with an in
side diameter of 20 mm is used to drain a wading pool as is shown in Fig. P3.5? If viscous effects are neglected. what is
the ﬂowrate from the pool? 2 2
1%+—\—/‘5+zl =!;+—’~— +22 23 2‘?
7710:,
e. 429?“, in) = (am/a
’ = 2.99%
0" . 4 3
Q = ,9: 14 =%(0.020m)2(2.9a—S”3) = q.” x/a g.— 3.6% Water ﬂows steadily with negligible viscous effects ( 1)
through the pipe shown' in Fig. P3. “Ht is known that the 4 " "
in. diameter section of thinwalled tubing will collapse if the
pressure within it becomes less than 10 psi below atmospheric
pressure. Determine the maximum value that h can have with
out causing collapse of the tubing. 4in. diameter thinwalled tubing 5 in.
(3) I FIGUHE‘P3.6I{ + +112, 2241“:
éL212g" *1 2—; iii/1:0 J V1150 szﬂq and ’0‘: WW" (”t—£3; Fvwoﬁ
”31 W] 2'15” 4 _ Jame/#1 V: .
419‘ W + 232.2 H/s‘) lé=4n7f$ J' .2; 3' 2;
Iii/Jere
£3:01 25'1”», “lid Y3=%=Qz “bl)LV: 2:13.) )(4/7‘Ei)
I; = m 5315‘
T as)
— — M
4H A + 2(32 iii/:1)
or 3.68 Water flows steadily from the large open tank shown in
Fig. P3.68. If viscous effects are negligible, determine (a) the
ﬂowrate, Q, and (b) the manometer reading. h. 0.10m
IFIGUHE [33:69 (a) From #79 BernaU/II' eqyafian
ﬂ, *2 ZIP V1+Ouzt "/72 +246) 1/2'24'6'22 Where fl =f1=og [4:0] 2" (ifmlaﬂdz’zgol
Thus 31‘26’14. , or (932', =5fpl/22 50 19M l/2=/2§2, ——....___‘ 0V2= 2(ﬁ8lmfs‘)(¥m) = 9.'36m/s
Hence,
Q: A1 V; = gmomﬂmm/s) :0. am mil/s rb) From Me Barney/If equ‘ion, f3 261116 *4”? 702+: 2(01/2"+6'Zs, Ill/76m 22=23andp2=0
so Ma {’3— =2;sz l6”) ‘ 2
Also ﬂay: =I43 v.3 SO'M‘H‘ Kai 751/2: (g): V; =(g:é;nm) 88‘M/35/3.99IHAS Hence
{)3 a: —2— (qqq Jig/maﬁa? emsﬁ (/3 sew/s) ]=  575500 AM»:2 (:1 H 13" 0, from 21/73 waﬂamefer;
p3 : — 6:95 +4310 (2)» +(o.ae/2)m) z (/33x/03A//p;3)h +(awx/0’Mn’) (2.04m)
= — I33x/03h + LVN/0" M»: where /7~m (2) Tim, From Eq:. (Hand (2):
~5.6£X/0¥/V/m2 .: /33)(l'73/7 */,77X/0¥/Vﬂ7]1 h = O.5.7.I+m 3.76 Water ﬂows into the sink shovm in Fig. P336 and Video
V5.1 at a rate of 2 gal/min. If the drain is closed, the water will
eventually ﬂow through the overﬂow drain holes rather than over
the edge of the sink How many 0. 4in. —diameter drain holes are needed to ensure that the water does not overﬂow the sink? Neglect
viscous effects. 3'
77) 0:, 3‘1; it A Isa, 0.47th diameter
holes M mews 4m fammmtmwww w
A“; 5. 5 K; 9.x {5 :‘gisﬁﬁgm .: s It; FIGURE 3.76 2. "~ ‘
£L+g+z = £6411sz , where £50, V,=0,Malz2_r=23=0 V
2,: g or V2=V2331 =[2(3101§)(L§%_33H)]z=2.5¥§ = n A; V2 = n 6‘ fdzzv where n= —number of holes re aired
c ?
d1 =0 4/» and C: contraction coon”. T/ws IANM (_J_____m:n 23m. m3 _ 3 H"
Q=2MM{6OSN)(194I ){ 17291.09) " ﬁg‘xm ﬂ; n Thus, 159/3: are needed. =0. 6! (see F], 3.1%) g «Q «(Mex/9"" #7:) "C.. d: V2. Was/J 71.:ng(25”%) = 3.30 3.79 Water is siphoned from a large tank and discharges into
the atmosphere through a 2in.—diameter tube as shown in Fig.
P179. The end of the tube is 3 ft below the tank bottom, and vis
cous effects are negligible. (a) Determine the volume ﬂowrate
from the tank. (b) Determine the maximum height, H. over
which the water can be siphoned without cavitation occurring. Atmospheric pressure is 14.7 psia, and the water vapor pressure
is 0.26 psia. 2—in. diameter (a) From fhe Bernoulli eqyaffoﬂ} $0.)
v” L 1/1
{9+2} *2? = @437; +3; , W/JEre f, 70150 and V, =0.
Thus)
2 = V: +2
I a} 2 HenceJ a
1 1‘
Mi. v1 = he“ Weiv move» (b) From the Barney/If equating 1r 2
6'3 +gﬁ+zs I ﬁfty; +341} Where 1/1516 5/1706 Qeﬂthsﬂal/J
and 2415/?
7771/5 we}, 23 ~23: ”we +3s wuss, 3
P3 +d”(2'3*22_) "1%: where #2. =' /’/.7’0$/‘a 0/96/79; =' 0.26/0“? Hence} 12 1A 144 '0?
(61‘7‘14—3N/Mzm = (Hiaux”; 7;}— or
H: 21.3 H ...
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 Fall '09
 MAE103

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