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**Unformatted text preview: **The University of Michigan Department of Mechanical Engineering ME 320 - Sections 1 & 2 EXAM II - December 10, 2007 Problem 1 (25 points) A solid circular cylinder of diameter D , length L and density ρ m is placed inside a hollow cylinder of slightly larger diameter, D + 2 h . When released, the metal cylinder is observed to fall slowly at a constant speed U . We want to calculate U , assuming that the air flow through the narrow gap of thickness h between the two cylinders is a steady laminar fully- developed viscous flow. The given quantities are: D , L , h , ρ m , ρ a , μ a , p a and g , where ρ a is the air density and μ a is the air viscosity. Assuming the air flow to be incompressible, (4 pnts) (a) Derive an expression relating the volume flow rate Q to U and other given quantities. (7 pnts) (b) If the pressure above the metal cylinder is atmospheric pressure p a and that below is p a + Δ p , derive an expression for Δ p in terms of U and the other given quantities....

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