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Hw 2 Solutions

# Hw 2 Solutions - 2.6 Bathyscaphes are capable of submerging...

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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) =50-5 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 v-1.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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Hw 2 Solutions - 2.6 Bathyscaphes are capable of submerging...

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