lect17 - Zoology 440 Biomechanics 2008 Lecture 17 Drag and...

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Zoology 440 Biomechanics 2008 Lecture 17. Drag and the Reynolds number. •Recap conservation of energy and mass •D’Alembert’s Paradox and the missing energy •A wake is a separate issue •The Reynolds number measures the relevance of viscous and inertial stresses Continuity: what goes in must come out (mass may not appear or disapear). Volume in /time u in A in Volume out /time u out A out ! u in A in = ! u out A out ! u/ ! x + ! v/ ! y + ! w/ ! z = 0 Conservation of Energy: what is the relationship between fluid motion and pressure? 1 2 u 1 ,h 1 ,P 1 u 2 ,h 2 ,P 2 P 2 / " + gh 2 + u 2 2 /2 = P 1 / " + gh 1 + u 1 2 /2 (P 2 - P 1 ) / " + g(h 2 -h 1 ) + (u 2 2 - u 1 2 )/2 = 0 (P 2 - P 1) / " + (u 2 2 - u 1 2 )/2 = 0 # P / " + g # h + # u 2 /2 = 0 Conservation of Energy: what is the relationship between fluid motion and pressure? (P 2 - P 1) / " = (u 1 2 - u 2 2 )/2
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D’Alembert’s Paradox (P 2 - P 1) / " = (u 1 2 - u 2 2 )/2 stagnation points u = 0, P = high u: high P:low No net force? D’Alembert’s Paradox
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lect17 - Zoology 440 Biomechanics 2008 Lecture 17 Drag and...

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