Final - Winter 2006

# Final - Winter 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 - April 17, 2006 Problem 1 (20 points) A long, flexible rubber tube is attached at one end to a reservoir containing incompressible fluid at gage pressure Δ p and is open at the other end to atmosphere at pressure p a . The tube is elastic so that its local radius is related to the local pressure in the tube according to, R ( x )- R o = α [ p ( x )- p a ] where R o denotes the radius at x = L , and α is a given constant. The tube has a length L and is attached to the reservoir with a bellows arrangement so that it is free to assume whatever radius the local pressure dictates. Gravitational effects are negligible. In terms of the given quantities: R o , L , α , Δ p , ρ and ν , ( 7 pnts) (a) Derive an expression for the volume flow rate Q in the tube, assuming viscous effects are negligible. What shape does the tube assume in a steady, equilibrium state?...
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Final - Winter 2006 - The University of Michigan Department...

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