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BENG3512007+Midterm

BENG3512007+Midterm - Biomedical and Chemical Engineering...

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Biomedical and Chemical Engineering 351 Engineering and Applied Science 551 FALL 2007 MIDTERM EXAM OPEN NOTES: OPEN BOOK: OPEN EVERYTHING except mouth. TIME LIMIT: 90 min. 1) The Strange Race (40 points): The following hypothetical strange race between an organism and a cloud of diffusible molecules takes place: The motile organism and a small, compact cloud of diffusible molecules are at the starting line and released simultaneously. The organism swims in a given direction at constant speed (u o ) and the molecules diffuse with constant diffusivity (D). A) We know the organism is going to eventually win this race but why? I need a rational mathematical explanation not a qualitative argument. Be very brief. B) The suspense in the race, then, is in figuring out how long it will take the organism to take the lead. Let u o be the constant speed of the organism. What is the time at which the organism pulls ahead of the compact cloud? C) Many small organisms from the size of bacteria to viruses can sustain a maximum speed of ten body lengths per second. Given this estimate what is the time required to in terms of body length (L) for the organism to pull ahead? What
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