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exam1-fall11 - The University of Michigan Department of...

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The University of Michigan Department of Mechanical Engineering ME 320 - Sections 1 & 2 Exam I - October 31, 2011 Problem 1 (17 points) Oil spills of various magnitudes may occur in ports where oil tankers are loaded or unloaded. The density ρ o of oil is less than that of sea water ρ w , and the two fluids are immiscible so that if an oil spill occurs, the oil will float on top of the water and spill sideways. To contain any possible spills and minimize pollution, a semicircular oil boom of radius R is deployed around the dock where the loading takes place, as shown in the figure. The boom is a vertical fence that floats in the water, its bottom being submerged in the water and its top extending above the water surface. It prevents the spread of oil beyond the barrier when the oil layer does not extend above the top or below the bottom of the fence. Suppose a volume V of oil is spilled inside the boom. After sufficient time for hydrostatic equilibrium to be reached, a layer of oil of uniform thickness h
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