Midterm - Fall 2007 - The University of Michigan Department...

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Unformatted text preview: The University of Michigan Department of Mechanical Engineering ME 320 — Sections 1 85 2 EXAM I — October 29, 2007 Problem 1 (20 points) A reservoir of water is closed at one end by a barrier. At the top of the barrier is an L-shaped channel that further restrains the water when its level is higher than the barrier top by the amount h, as shown in the figure. The channel is hinged at the corner point 0, so that it can rotate in a counterclockwise direction, but not in a clockwise direction. If the water level is high enough, the water force on the vertical face of the L—shaped channel will maintain a clockwise moment that will exceed the-counterclockwise moment of the water force on the horizontal leg of the channel, and the channel will remain upright and prevent water leaking beneath it. ' (8 puts) (a) Assuming that the water in the reservoir has a uniform density of pw, calculate the minimum value of the ratio h / H that will ensure against rotation of the L—shaped gate. (12 puts) (a) Now consider the case where the water in the reservoir is a salt solution which has a. density which increases linearly with depth from a value of pm at the free surface to a value of 1.5pu, at depth h. Calculate the minimum value of the ratio h/H that will ensure against rotation of the L—shaped gate in this case. Problem 2 (20 points) A scrubber is a device which removes pollutants from air by allowing the air to pass through a spray of water droplets. The pollutants are absorbed by the droplets, and the air that passes through is clean. An inventor designs the scrubber shown in the figure, which has the advantage that no fan is needed to force the air through the spray of water. A high speed water jet, of speed and mass flow rate mm, enters at station and quickly breaks up into droplets which become dispersed in the tube. By station (2), friction between the water droplets and the air has brought the two phases to essentially the same uniform speed V8. The device automatically draws in air from a source at atmospheric pressure and density via the disk-shaped entrance, whose radius is large compared to the radius R of the mixing tube. The known parameters are Vj, V5, mm, pair, and R. You may neglect the viscous forces between the sidewalls of the device and the fluid flowing inside. You may also assume that rimw >> ma,“ where mm, is the mass flow rate of air drawn in. (2 pnts) (a) Explain in words what causes the air to be drawn in to the device through the disk shaped entrance. (10 pnts) (b) Find the-pressure at station (8 pnts) (c) Find the mass flow rate of the air, mm, drawn through the device. (ME 310 * 5mm 1) I ‘ L1H h' I (9' was) 50' “F? Fa 2007 I! P-Pams 4/; Z— L’ng 23' i ~ 1;“ k—ICOV 7 E+og>¢®§zi‘ a z , 4 T , h ‘ *5ng ‘kwg __ k ,. , 13mg, { IJéQngh — 1.930312 +_ owe—“:32; 4 (2(0). 5,11 ,;.,)-u;(9wak~b+\ 4,. M- fl: f- ~ 2 ‘ i l i ‘1 1 1 ‘4’"— i \ < I i \ l L l ' Wm“; __‘ __w..<.+u~.-.-l~ ‘4” .32--..» “QM..-” «NHL... 41 $214., 3 1;. ":_ g z i 42482 100 SHEETS nun-1- u, s, A. w n'o'\b on CO—h’f Off? Bernouflg Q @ km FEM 6H”? , din'o'lLiOh, dc. 2—182 ‘00 SHEETS )M. J IU/l r: 1:: mn L .mld / . . 15 @dfiwxl, Sinuz; figu CUR. Brnowaex' 10 G Sig/Kc: Tinwz. {01:} 1“ a agar» 03W +0.1. M'jor Prmure (Ln? L5 M '{o 04-, my; (PHYS 3 [S FMOuuixy) mofl P4 - CIR) fl+;m/§'=V+Lvl Q 4‘ z“ o “F. a v ~V ‘ETFWVLF L". gig—f). =- h‘w Q Inga =fi vtfi = a flaw v- “v6 @ ...
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Midterm - Fall 2007 - The University of Michigan Department...

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