LME_PracticeProblems - Practice Problems on the Linear...

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Practice Problems on the Linear Momentum Equations C. Wassgren, Purdue University Page 1 of 49 Last Updated: 2010 Sep 16 COLM_01 A frequently used hydraulic brake consists of a movable ram that displaces water from a slightly larger cylinder, as shown in the figure. The cross-sectional area of the cylinder is A c and the cross-sectional area of the ram is A r . The ram velocity, V , remains constant. Assume that the gap between the cylinder and the ram is much smaller than the displacement of the ram x . a. Determine the water velocity as it leaves the cylinder. b. Determine the force F on the ram in terms of A r , A c , and V . Assume that the cylinder is initially full of water, that gravitational effects are negligible, and that the water exits the cylinder to atmospheric pressure. Answer(s): 1 out 1 c r cr r VA A A A      2 3 2 2 rc AA FVA A    x V F A c A r water filled cylinder
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Practice Problems on the Linear Momentum Equations C. Wassgren, Purdue University Page 2 of 49 Last Updated: 2010 Sep 16 COLM_02 A sonar buoy is being tested in a wind tunnel with a circular test section as shown in the figure. The air in the tunnel has a density of 1.2 kg/m 3 and the test section radius is R = 0.5 m. Measurements at location A indicate that the incoming velocity is uniform with a velocity of U = 10 m/s while the downstream velocity, measured at location B, is zero at the centerline and increases linearly with radius, r , measured from the tunnel’s centerline. A U-tube manometer filled with water (with a density of 1000 kg/m 3 ) is used to measure the pressure difference between sections A and B (the pressure is assumed uniform at each section). The elevation difference between the two legs of the manometer is H =0.03 m as shown in the figure. a. Determine the maximum velocity, U max , at section B. b. Determine the drag acting on the buoy. Answer(s) : 3 max 2 UU  2 22 2 drag H O air 8 F gH R U R  F drag = water R r U Section A Section B H
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Practice Problems on the Linear Momentum Equations C. Wassgren, Purdue University Page 3 of 49 Last Updated: 2010 Sep 16 COLM_03 An incompressible, viscous fluid with density, , flows past a solid flat plate which has a depth, b , into the page. The flow initially has a uniform velocity U , before contacting the plate. After contact with the plate at a distance x downstream from the leading edge, the flow velocity profile is altered due to the no-slip condition. The velocity profile at location x is estimated to have a parabolic shape, u = U ((2 y / )-( y / ) 2 ), for y and u = U for y  where is termed the “boundary layer thickness.” 1. Determine the upstream height from the plate, h , of a streamline which has a height, , at the downstream distance x . Express your answer in terms of .
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This note was uploaded on 10/01/2011 for the course ME 509 taught by Professor Wereley during the Spring '11 term at Purdue University-West Lafayette.

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LME_PracticeProblems - Practice Problems on the Linear...

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