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Unformatted text preview: The University of Michigan Department of Mechanical Engineering ME 320  Sections 1 & 2 Final Exam  December 15, 2011 Problem 1 (23 points) Two thin rectangular plates, of length L and width w into the page, are connected at one end by a closedend flexible bellows arrangement, as shown in the figure. The parallel plates are separated by a distance h ( t ) which is decreasing at a constant rate dh/dt . The flow between the plates can be assumed to be highly viscous (inertia free) and incompressible. The plate width w is much greater than the length L and dh/dt is small, so that it can be assumed the flow between the plates is unidirectional along the x direction with volume flow rate Q ( x,t ). The pressure at the outlet x = L is atmospheric pressure, p a , and the fluid density is ρ . The given quantities are ρ , L , w , h ( t ), dh/dt , and p a . (3 pnts) (a) Find the volume flow rate per unit width, Q ( x,t ) /w . (9 pnts) (b) Find the pressure distribution, p ( x,y,t ) between the two plates. You may neglect gravity....
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This note was uploaded on 12/16/2011 for the course ME 320 taught by Professor Chin during the Fall '08 term at University of Michigan.
 Fall '08
 Chin
 Mechanical Engineering

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