exam1_2019_soln.pdf - ECH 141u2014Fluid Mechanics Winter...

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ECH 141—Fluid Mechanics Winter 2019 Exam 1 (Closed book, no notes) 1. (20 pts.) An object that is denser than water weighs A in air and weighs W when completely submerged in water. What is its specific gravity? Explain your answer.
2. An emulsifier is a device that is used to disperse oil droplets in water. (Similar devices are used in bioprocessing to “disrupt” or break up cells in order to harvest target proteins inside them.) Typically a mixture of oil and water flows at velocity U through a channel and up to a plate, and then is forced at high pressure through a small gap with height h. The density and viscosity of the water are ρ and μ , respectively. In order to create small drops from large ones, they must be stretched until they break, and the oil/water interfacial tension γ opposes this extension. The property used to evaluate the performance of an emulsifier is the mean diameter D of the oil drops exiting the device. It has been found that D is insensitive to the much larger diameter of drops in the oil/water mixture entering the device. In addition, although the ratio of the oil viscosity to the water viscosity is a dimensionless group that obviously impacts performance, that ratio changes by so little in practice that it is not of interest here.

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