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Midterm - Fall 2006

Midterm - Fall 2006 - The University of Michigan Department...

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Unformatted text preview: The University of Michigan Department of Mechanical Engineering- 'ME 320 - Sections 1 Sc 2 Exam I” - Nov. 1,2006 _ I Problem 1 (10 points) \\\\\\\\\\ \\\\\\\‘ mg; I - \\\\\\\\\\\\\ A plate of weight W per unit width is suspended at one end by a hinge at the ‘water level of a. reservoir as the ﬁgure. The bottom end is' free to move in a circular arc of radius R ' ' I In terms of the given parameters: (10 pnts) Derive an expression for the equilibrium angle of the plate, 6', with respect to the vertical. Problem 2 (15 points) W018!" A barrel of cross-sectional area. A5 and height H5 containing toxic oil of density" poi; has been thrown illegally into a pond. The barrel sits on the bottom of the pond surrounded by water, as shown in the ﬁgure. Two holes on the side of the barrel, I each of area Ab and separated by a height H , allow the water to enter the barrel ‘ through the bottom hole and oil to leak out through the top hole. In your analysis, you may assume Ab >> Ah and quasi—steady ﬂow. The given quantities are: pm, pail,A¢,,Ah,Hb, H and g. puts) (a) Explain in words the physicalbrigin of the force which drives the oil out of the barrel. (8 put) (b) Derive an expression for the velocity V of the oil through the top hole when the oil/water interface is at a distance h below the top hole. (6 puts) (c) Find the time it takes for all the oil to leak out of the barrel. Problem 3 (15 points) A gas turbine engine is being tested under steady ﬂow conditions in the rig shown in the ﬁgure. The engine is mounted on a strut which makes an angle a with the vertical. Under running conditions, the engine draws ml kg/ sec of air of density p; at its intake and burns fuel at a mass ﬂow rate of ﬂy kg/ sec. The exhaust products have a density p2 and leave the engine at section 2. The areas of the intake and exhaust ' are both equal to A and the atmospheric pressure is pa. In terms of the given quantities: m1,m,e,p1,rh02, A and pa, (4 puts) (a) Find the inlet and outlet velocities V1 and V2. You may assume that both velocities are uniform across their respective cross sections. (3 puts) (b) Find the inlet pressure pl. (8 pnts) (c) Find the tension force T in the diagonal strut. \$3 3,; x. H chi “Cola—Tm“: - 4| , g a...” I "mum mans um um I .‘V- I J “‘3‘ 12%? “.3, A, Jug: Zane. . é f. 31. ME ii" 9i .;i a? 3? I 2m.» 24. 26 , a-%w\.\+n.u._ﬁ... +..._It 4.32? 2-5 0% u > 4. A Majw _ m 93¢ ﬁu¢u-na§r I}...th 7o J. 9 ¢ % 33:3 Hun... . . c... a“ 9 egg gagging. ﬂue “.346:er almv. «a: . v"... v“; ﬁrm @ _ M . H. mm .3”: . :0 1+ 553 i. T. 555%.... mug 1+ h. u Ha anew-w no” ER M; .N \$.ch “ E..er \$0 .53. of Caﬁddsﬁulx 44+ z... (hangs. w (casual—3U AUU .55 4i .+ mm 001 uer , , _ ...
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Midterm - Fall 2006 - The University of Michigan Department...

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