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Exam4_2008_Solutions

# Exam4_2008_Solutions - NAME 0 Lu Y\QN-E Ofﬁcially...

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Unformatted text preview: NAME ' 0 Lu Y \QN-E; Ofﬁcially Enrolled in MB or BME? (circle one) Fluid Mechanics Exam 4, Spring 2008 There are 4 problems on this exam: Problem I: 20 points Problem 2: 10 points Problem 3: 10 points Problem 4 : 15 points OR 20 points By signing below 1 agree to abide by the following honor code: As a member of the Northwestern community, I will not take unfair advantage of any other member of the Northwestern community. I speciﬁcally agree not to reveal to any other student the contents of this exam. Signature: Date: -————o—-—————.~___..___.________________ At the end of the exam, please use the big magic marker to write the ﬁrst four letters of your last name in the four boxes below as you sign out. Thanks. Front Page Exam 4, Spring 2008 page 1 Probiem 1) A rectangular tank of height H, length L, and width W is ﬁlled with a ﬂuid of speciﬁc weight 7. For all parts of this problem, Work in absolute pressure, assuming that atmospheric pressure is PLm A. (3 points) Write an expression for pressure as a function of depth (2) in the tank. Use the coordinate system shown, with the location (0,0,0) at the location shown. Remember Em P7» P06» = (03 (it—33 + Pew B. (4 points) Write a double integral to ﬁnd the total force due to pressure of the ﬂuid on the wall of height H and width W. Maintain the location of z = 0 that you used in part (A). You do not need to solve the integral. You will be graded only on how you have set it up, including limits of integration. Remember Em N l—\’ l' \ “51-1 d — . _. (g: [/33 u 2, + \ twirl?) X SR? AR Fﬂ' WM ,9: WW j, Porh‘l' -§P ﬂack LOT: ”500% \$.39 1L plant-\— {:34- CprrﬁclA‘f cothfwa pvﬁSw-Q weep-hkp‘) l“ C (4 points) Solve the integral you wrote in Part B. If you set the integral up wrong, you will get this part of the problem wrong as well Set it up correctly! 0 O you wea- 3th my \ Mudv CMC‘V MSW 0‘“ M‘r, Exam 4, Spring 2008 page 2 D. (3 points) Write a double integral to ﬁnd the total force due to pressure of the ﬂuid on the floor of length L and width W. Maintain the coordinate system and the location of z = 0 that you used in part (A). . Remember BM u VJ H (Ma dreamy A5 is - wk Q 3»: maids 4%” Wreé 9M outlaw lb “trim“ \ FW‘JV {V cleaver lac—w Lads awed E. (2 points) Solve the integral you wrote in part D. (ﬂex—M‘gwu (\0 Wise-K W4C F. (4 points) Now change your coordinate system so that z = 0 is now at the Log of the tank. Write an expression for pressure as a function of depth (2) in the tank. Remember to continue to assume that atmosgheric pressure is Pa“ :3 Exam 4, Spring 2008 page 3 1.136%}? ﬂash 1"; B ETA 2(10points) W50 2: vim-H» ”PM «av-Q W A (4 points) In the table below list the tow assumptions necessary to apply Bernoullis equation. When possible write a mathematical expression that exp1esses that assumption: Math expression that describes the assum tion if oss1ble M‘J‘Sui no \J tseoskdg K N“ O 5.9... 6::34'Kx6 aq‘wc— 'a Weds city/ﬁt at = 5: N21: \n—LWV‘QS5\5LL« QKU‘NA j— W C B B. A giant vat of height 10 meters and width 6 meters contains water with density p = 1000 kg/rns. The vat has a tiny hole poked in it right in the center of the 6 meter wall, at a height of 6 meters from the ground. Assume that all conditions necessary to apply Bernoulli's equation are met. i. (3 points) What is the speed of the jet of water as it emerges from the hole? %* 213%“ me =- P4 o 3‘31. ¢ :0 +93) [4 web—- if“)? ii. (3 points) What IS the speed of the jet of water when it hits the ground? /E/J°1V:n°- /" “PW " M O (9 1% 0° "*7 Exam 4, Spring 2008 page 4 3. (10 points) A. (6 points) Water ﬂows through the pipe contraction shown in the ﬁgure . For the given 0.2-m difference in manometer level, determine the ﬂowrate as a function of the diameter of the small pipe, D. Assume that all ofthe conditions necessary to apply Bernoulli's equation are met. S¥wawla \$®MLQ '% OJ : r 15% maé 1” F2*'§fV»?+a-a’iz . e» " 9* V” S I Zqu‘l. £1217..- PJr a we; : w:- a =ﬂ6C“'23 Mme) .1 _4,__, ‘— or B. (4 points) A fountain emits ajet of water that shoots straight up vertically from the ground 1 with initial velocity V0 How high above the ' . ground does the ct '? ' ' necessary to apply Bernoulli are met. J g0 Assume that a“ COHdlUOﬂS 2—";H Ptio H Exam 4, Spring 2008 page 5 4. Choose to solve ONE of the following problems Choice One (15 points) A stream of water with diameter Do emerges from a faucet with a velocity V0. The water falls vertically to the ground a distance H below What is the diameter D] of the stream when it hits the ground? Assume that all conditions necessary to apply Bernoulli are met. Your answer may not include any Variables other than Do, V0, g, H, and D1” but it might not need to include all of those. Choice Two (20 points) A stream of water with diameter Do emerges from a faucet with a velocity V0. The water falls vertically to the ground a distance I-l below. What is the diameter. D(x) of the stream as a function of the distance x below the faucet? Assume that all conditions necessary to apply Bernoulli are met. Your answer may not include any variables other than Do, V0, g, H, x, and D001 but it might not need to include all of those. Circle which problem you are solving: CHOICE 1 CHOICE 2 A: 8-“ I» ' eavo'ﬁla )4 X - #14 — - poet “(*5 3 fmvﬁs ‘9“ rem—NB, ‘3‘ an by . be: a f”"””‘ a: ...
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Exam4_2008_Solutions - NAME 0 Lu Y\QN-E Ofﬁcially...

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