Final - 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 & 2 Exam II - Dec. 13, 2006 Problem 1 (20 points) A thin, flat plate of width w is dipped into honey of density and viscosity to a depth L and subsequently pulled out. It is then held stationary in a vertical position while the honey drains from it, as shown in the figure. The thickness h ( x, t ) of the fluid film increases from top ( x = 0) to bottom ( x = L ) and decreases with time as the fluid drains away. Assuming that the flow of honey is highly viscous such that fluid inertia and acceler- ation are negligible, (10 pnts) (a) Derive an expression for the volume flow rate per unit width Q ( x, t ) /w in the film on one side of the plate, as a function of the film thickness h ( x, t ) and the given parameters. (10 pnts) (b) Assuming that the free-surface of the layer of honey on the plate retains a parabolic shape h ( x, t ) = h ( L, t ) radicalbigg x L , use the principle of conservation of mass for a control volume drawn around the...
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Final - Fall 2006 - The University of Michigan Department...

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