lect23 - flow is reversible flow equations are linear...

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Biology 427 2007 Lecture 23. Life at Low Reynolds Numbers •Recap High Re Number Swimming •Low Reynolds Number Phenomena •Ciliary locomotion •Dilemmas about force generation •Regulation of cilia and flagella Thrust = C D ! S u 2 /2 + “something else” = C D ! S u 2 /2 + "! V du/dt “Drag” = C Dbody ! S body u body 2 /2 + " body ! V body du body /dt Balance of forces ( thrust and “ drag” )for a swimmer! Thrust = Drag a small reading from Vogel a demonstration A reading and some movies
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m du/dt = -6 ! R μ u 3 μ m 0.03 mm/s E. coli: how far does this glide? Swimming at Low Reynolds numbers (<1) Phenomenological issues:
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Unformatted text preview: flow is reversible flow equations are linear inertia is negligible disturbances are manefest over huge relative distances. boundaries are all important shape matters considerably less A sphere: Low Re High Re C D = 24/Re 0.1 D = 6 ! r m U 0.1 0.5 r ! r 2 U 2 2 ! &quot; U l ln(l/a) - 0.897 D = 4 ! &quot; U l ln(l/a) + 0.193 D = Two important questions: What are the cellular mechanisms that generate force? What are the fluid dynamic mechanisms that propel the animal?...
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This note was uploaded on 06/03/2008 for the course BIOL 427 taught by Professor Daniels during the Spring '08 term at University of Washington.

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lect23 - flow is reversible flow equations are linear...

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