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lect16 - Zoology 440 Biomechanics 2008 Lecture 16 Basic...

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Zoology 440 Biomechanics 2008 Lecture 16. Basic fluid dynamics: defining properties of fluids. •Recap definition of a fluid and Newton’s law of viscosity. •Conservation of mass and continuity •An applicaion of continuity •Conservation of energy and Bernoulli’s principle •Applications of Bernoulli Recap A fluid deforms continuously under an applied stress no slip condition ! = μ du/dy dynamic viscosity of a fluid Newton’s Law of Viscosity " = kinematic viscosity = μ/ # ! = " d ( # u) /dy ! du/dy viscosity depends on •temperature •concentration of dissolved solutes •shear rate (rate of strain) 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 http://home.earthlink.net/~mmc1919/venturi.html
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Aorta Area 1 cm 2 Aorta velocity 10 cm/s Capillary velocity = 0.1 cm/s Each capillary has 5 μ m diameter How many capillaries ( N ) ? % u in A in = % u out A out u aorta A aorta = N u cap A cap N = u aorta A aorta /(u cap A cap ) = 10/ (0.1 ! 2.5 2 10 -8 ) " u/ " x + " v/ " y + " w/ "
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