Final - Fall 2005 - The University of Michigan Department...

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The University of Michigan Department of Mechanical Engineering ME 320 - Section 1 Exam II - Fall 2005 Problem 1 (20 points) A highly viscous liquid of density ρ and viscosity μ slowly seeps up through the porous floor of a rectangular channel which is open to the atmosphere above, as shown in the ±gure. The porous area of the channel has a length L and width b and the liquid ±lters up with a uniform speed V through the porous area to form a liquid layer which then moves horizontally from left to right with a velocity distribution u ( x, y ). The channel is closed at the left end x = 0 and extends to the right beyond the end of the porous section, x = L . The fluid thickness h ( x ) decreases with increasing x ,and reaches a value of H at x = L . In terms of the known parameters p atm. , g , ρ , μ , b , L , H , V and the unknown layer thickness h ( x ), derive expressions for: (4 pnts) (a) the volume flow rate Q ( x ), (2 pnts) (b) the pressure distribution p ( x, y ), and (8 pnts) (c)
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Final - Fall 2005 - The University of Michigan Department...

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