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Unformatted text preview: 2.6 Bathyscaphes are capable of submerging to great depths
in the ocean. What is'the ptessure at a depth of5 km. assum
ing, that seawater has a constant speciﬁc weight of 10.1 kN/m’?
Express your answer in pascals and psi. #:3’1 +43
4:! ‘/he Jurﬁze. f3 =0 so 771d 6
75: (/a,/x103;,%){5‘xm3m) =505 x/o A: (In (fault) , *210 In a certain liquid at rest. measurements of the spe 60 107
ciﬁc weight at various depths show the following variation: 70 110 80 112
ﬁ _ 9o ‘ 114
h (ft) 7 (lb/ft”) 100 1 15 h
o 70 :8 g: The depth h = 0 corresponds to a free surface at atmo 30 91 spheric pressure. Determine, through numerical integration
40 97 of Eq. 2.4, the corresponding variation in pressure and show 0 102 the results on a plot of pressure (in psi) versus depth (in
5 feet). d..
£~X Lef 2‘: {0”2 [Ire Ay'qre) S:
77701: c/z=—dh and 771tre1$rp o/P: vkd? = 3"dh where 7!; 11s 7712 pressure ai‘ ole/2771 42;. Efmel'lb’l (I) C411 be 15427/21‘14/ numerical/9 quj
715 fl’d/Deaal'a’a/ I’Hlf’ C9.) 01! Ware 5,, 3' ) Xm h, 4”,; n = number 4; 0/444 700/55 . 771: foju/M‘e/ rem/7": are 714/04 Ive/and, d/Onj 111/771 7716 Pressure, p (psf) 6000 4000 2000 cor/afmd/b p/o't of presSure v5. 0’9p771. h(ft)
o
10
20
so
40
50
60
7o
80
90
100 y, lblft"3 Pressure,psf 70
76
84
91
97
102
107
110
112
114
115 0
730
1530
2405
3345
4340
5385
6470
7580
8710
9855 Depth, h (ft) Its 4.5 Amo—dimemiomlvelacityﬁeldhgimbyu=l+yand
v1.Deminctheequadonofmestreamllmthatpmes
mmughtbeodgin. Onngraph.plotthismnmline. u r. My and IV =/ so {be dream/Mes are 7W9” 5/ d I Tim, (“WHY {fr/X or y+éy1 sx +C’ killer: CI} dam/007’. For Me dream/Me {lid goes {II/W7}? Xsy=0J 6:0.
Hence, x=y+iyz 771/3 dream/I'M is ,o/vz’fe/ Ae/aw. A/ofc {ha/ .r/bce Ar =/>01 {be
(ﬁred/an of flow i: as show». 4.8 The velocity ﬁeld of a ﬂow is given by What is the angle between the velocity vector and V = 20y/(x1 + yz)“li — 20.7t/(x2 + f)”; ft/s. the x axis at points (x. y) = (5. 0). (S. 5), and
where x and y are in feet. Determine the ﬂuid (0, 5)?
speed at points along the x axis; along the y axis.
2 20X
a = —————°" (x14. w)”: ’ V =— (x2 + y‘)” 7770:, l/==1/L("*Vz or V: 400x“ +¥OOZLJJ§ (x’wy‘) = 20? ’W‘ W by [4/30, ~2ox y (5 5)
1., 1911 fan 9 ” "y = (—XzL—_x o 5 or U (X‘fy‘tyi ( ’ ) +an€=~§ 77mm, {or (X,y) =(6', 0)
ﬁner~00 or 0" “90° for (w) =(5,5) Av
fan0= '/ or 0=;5° for (X, y) =(0,s)
fanO = 0 or 9= 0 0 4." As shown in Video V4.6 and Pig. Full. 3 ﬂying airpiane
produces swirling ﬂow near the end of its wings. In certain cir
cumstances this ﬂow can be approximated by the velocity ﬁeld
a = ~Ky/(x’ + y’) and v = KX/(xz + y‘). where Kis acon
stant depending on various parameter associated with the air
plane (i.e.. its weight. speed) and x and y ate measured from the
center of the swirl. (a) Show that for this ﬂow the velocity is
inversely proponional to the distance from the origin. That is.
V = K/(x2 + y’)"’. (b) Show that the stneamlines are circles. 1/ '_ _ My)1L (er
(a) V: “2+”:  [WP +(X—1+—Y1P 0r V= é, where r=W = (b) 57'ream/inos are git/en by £1 . all .5 xii?)
Tkw’ (x1 + ya)"
yd), = Xa’x w/Iic/i w/IM inky/u {94 W63 f7: = "Hy+5], Were 5, I} ace/triad
ar X1+Yzz Com/Mil ...
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 Spring '09
 Daley
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