Shapiro1.05_Problem - p a the gas length l is l The...

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MIT Department of Mechanical Engineering 2.25 Advanced Fluid Mechanics Problem 1.05 This problem is from “Advanced Fluid Mechanics Problems” by A.H. Shapiro and A.A. Sonin Cylinder with gas trapped The sketch shows an inverted cylinder in which gas is trapped between the closed top and a frictionless piston of weight W p which is free to move. The cylinder /piston area is A , and the thickness of the cylinder may be taken as negligible. The gas in the cylinder is an ideal gas which maintains itself at water temperature. When the cylinder is held horizontally in the ambient atmosphere, which is at pressure
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Unformatted text preview: p a , the gas length l is l . The cylinder is weighted at the bottom (total weighted W c ) so that it rides in a vertical position when placed in water. The water density is ρ . • ( a ) Derive expressions for the gas space length l and submergence h of this device when it is in a static equilibrium position totally submerged in the water. • ( b ) Is this static equilibrium position stable, unstable, or neutrally stable? Prove your answer. 2.25 Advanced Fluid Mechanics 1 Copyright c ± 2010, MIT...
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