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Unformatted text preview: 2.57"! The open U—tube of Fig. P2917 V is par
tially ﬁlled with a liquid. When this device is ac
celerated with a horizontal acceleration, a, a ‘
differential reading, h, develops between the ma
nometer legs which are spaced a distance Bapart.
Determine the relationship between a, L', and h.  FIGURE P237 2‘100 .———__—__—_‘—_—_A_—.___—_._._.___~ V
j—ﬂm
__ , , 3.1 Water flows steadily through the van2
able area honzontal pipe shown in Fig P3 1. The "
velocxtv1s given byV V = 10(1 + x)i ft/s, Where 1 ’
1 is in feet. Viscous effects are neglected (a) De
termine the pressure gradient «Sp/ax, (as a func :It1on of x) needed to produce this ﬂow. (b) If the
gipressure at section (1) is 50 psi, determine the
ipressure at (2) by: (i) integratiOn of the pressure
Iggradient obtained in (3); (ii) application of the ' FIGURE 113.1 "
{'Bernoulliequation. ' (a) Jam—55% —— 91/111111 9:0 427/ 1/=/o(/+x) H/s
M = “pvﬁZ or 131%: ~§5r9V V=~p(/o(/+X))(/o) 63 Times; 752%: «Awfﬁéa: {292‘ (rm) ) WW7 X [/2 feet f1? XZ" :3
(11m % = 39mm 501141 » f44 = —w 1 (1+de
X ”5:5va XI: 
1
0/“ £2: 50/05" "' /76’(~3 +% ?I"§ (H /I¢;,:hz : 50 "/011/ #313”; I (1/) [4+2 2"p1/ +34; zip 4212(91/7' +1122 0,1 WW; 2 :22 ﬂ ”ﬂ +32“€(V,2"V lé") whens. 1/": /0(/+0) /o.££#
1/= /0(I+3)= 510/
i This ,0 ssopsz 1; (/95‘"7/%)(/o M‘J—éé (~— 7’ng2) =3217g1; IWWW._ j :m It can be shown that if viscous and grav—
itational effects are neglected, the ﬂuid velocity
along the surface of a circular cylinder of radius
a is V = 2V0 sin 0, where V9 is the upstream
velocity and s = a0 is the distance measured
along the streamline that coincides with the
cylinder (see Fig. Pill). For a ﬂuid of density p,
determine the pressure gradient in the radial dir
ection, ap/ar, on the surface of the cylinder.
Assume the axis of the cylinder is vertical. Is
@p/ ar positive or negative? Explain physically. For
what 0 is ap/ar the maximum? Explain why. 44.: mg .__ 37% ..m,%:§Fgg— =4; mt dz 
so Mai 3” .. 0
Aﬂ 1 1
er “5 3% = 33—»: Where V=2\{, sine and ﬂ=a Tbl/s
313:1“) V2 .si/J :L/a Note 'l/ml.‘ for" any Iacaﬁon (ale. 9) i/ {iv/kw: Mat $327 >0, ewe/J at a: 0 or 6: Isadey where 7!} —0 {’2 MVJ‘f ﬁat/e ﬂ1>fl if {/0121 is 7‘0
follow" a curved pail), excepf where
V"0 (as a} 0‘0 or 97/30489.) Maxi/MI» 91% occur: art :9: Qodey (ale. maxi/”VIII 0)" 51/29)
since #m’ i: rfﬁe mama of mummy Ila/Wa/ awe/eral/M. 39 3.13 As shown in Fig. P3.13 and Video V132, the swirling
motion of a liquid can cause a depression in the free surface.
Assume that an inviscid liquid in a tank with an R = 1.0 ft ra
dius is rotated sufﬁciently to produce a free surface that is
h == 2.0 ft below the liquid at the edge of the tank at a position
_. r = 0.5 ft from the center of the tank. Also assume that the liq
uid velocity is given by V = K/r, where K is a constant. ta) ‘
Show that h = K2 [(1/9)  (l/Rz')]/(23). (h) Determine the
value of K for this problem. : V2 2
3% t 0,. aﬂe
7711/3"; 100 1
[WM «é? ar am”
10 r
Bui ffz’i'h and f9=0 m‘ rm {be free surface.
,Tél/S: J an: ~P—‘Kfa —L :1 or My, 3‘ll 3.3.0 Water ﬂows through the pipe contrac
tion shown in Fig. P330. For the given 0.2—m
diﬁerence in manometer level, determine the ﬂow
rate as a function of the diameter of the small
. pipe, I). ‘ FIGURE, PéEQ, .
, we at v: " '.
va +2, =4+~ +3.:1 or viz/2% 2,:22 4M V1=0 a" 2; 2? bullf)’ 3.37%, and f1: ad/kg 50 {ﬂat ﬂ,”/2 =5 J'(é/’hz)=o'2aa :y
77105:, ' i I y' Wzl/Zig‘aé‘b: =1/zg(0.2.3
or Q zﬂzvz .; .gDZVZ. = ‘71‘201 V2K¢8/)(0v2) = A‘sy Dz 1%" W56” Div)”, 3~27 ' 3.43:3— 333 A smgoth plastic, 10—m~lon’g garden hose with an in
side diameter of 20 mm is used to drain a wading pool as is
shown in Fig. P143. If viscous effects are neglected, what is
the ﬂowrate from the pool? FIGURE P3. 6‘3 v,’ p: x ,7 , ,* , ~2
ﬁlePE‘FE, =7+~i7+22 W 3/"? fi’fz'o’, Z/“o' ”I
22 = ~023mj and 16 =<97 ,3 60 I ‘ . 3 60 Wate1 ﬂows from a huge tank as shown in Fig. P3. 60 At—
mospheric p1essure is 14.5 psia and the vapor piessme is 1.66
psia. If viscous effects we negl° cted at what height h, will caw itation begin? To avoid cavitation, should the value of DI be in cmased or decreased? To avoid cavitation, should the value of
D2 be increased or decreased? Explain. FIGURE P3. 60 Q + 19— +20 = ~33" + Z; + z, where ,0, =/#.5/os/a,ﬂ 3 L60 NW;
295/7 , 2,30, and V050 h=L1f2+.—__ ' (I) Combine 575. U) and (7—) 1‘0 obiﬂiﬂ.
_______1°a ‘7
h: Kari1P D1 2)}7 0/" [A . .2
h‘ z (”295 #Wf‘) « l¢8 A
6f; ("5195",; l] ’b '21»; ‘ 4T“: (3) From [7 [3) 111/: seen 1%41‘ )7 increases in Mamas/lag D
and decreasing D , Thus 1‘0 avoid cal/11142900 (a: A {a have
A smal/ 3001/95) D, shag/d be increased and D1 decreased. 3°60 In 3.94 Water ﬂows in a rectangular channel that is 2.0 m wide as
shown in Fig, P394. The upstream depth is 70 mm. The water
sulface rises 40 mm as it passes over a portion where the chan— nel bottom rises 10 mm. If viscous effects are negligible, what is
the ﬂowrate? " FIGURE $53. <24 2. 2 > ,
ﬂ+—Z’— +z,=£%+‘YE‘+Z W549i“? 79:0) [1:0, 21'50.0707, (I) a" 2 2
(Y 29 5 My 22 ..: (0,0/ +Q./o)m = 0.//m
Also I A, V = I42 V2
or b o 07 77711.5, E; (I) becomes
[;~0.71]V,’=2(4.31%)(av—0.079;» or V,= xzygl
Hence; QW‘LV, ‘= (0.07m)(2.t?m) (1.261%): O. 774 .2223 ...
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 Spring '08
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