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Unformatted text preview: Zoology 440 Biomechanics 2008 Lecture 15. Basic fluid dynamics: defining properties of fluids. ! here we have been and where we are going W ! he formal definition of a fluid T ! iscosity and its determinants: temperature, V concentration of dissolved or suspended solutes, even shear stress (non Newtonian characteristics) ! he problem of nectar feeding T ! ontinuity (conservation of mass) C Solid and structural mechanics: stress and strain distributions, movements of bodies and their parts in response to muscle forces and gravity.! Fluid dynamic issues underlie: ! Internal flows (blood, respiratory flow, liquid food...) ! External flows (swimming, flying, running in air and water) ! Wind and water forces on sessile creatures ! Dispersal ! Transport of nutrients and heat to and from biological surfaces Definition: A fluid deforms continuously under an applied stress.... Definition: A fluid deforms continuously under an applied stress The continuum hypothesis will dominate our studies: density, temperature, momentum, energy ... all vary continuously. We can actually calculate their spatial derivatives if we have to. But, when the spatial scale of the problem (L) is of the order of the mean free path of the fluid molecules (!), we have a problem. Knudsen number = !/L. This underlies many subcellular problems and remains rather unresolved! "L! ( = d%/dt! F! du/dy = d%/dt! Solid ( = du/dy ! dynamic viscosity of a fluid! Newton's Law of Viscosity! F ~ "L! # $ %! # = & %' spring "L! F! Fluid F ~ "L/"t ~ dL/dt! ( $ d%/dt! ( = d%/dt! dashpot Recap A fluid deforms continuously under an applied stress ( = du/dy ! dynamic viscosity of a fluid! Newton's Law of Viscosity! )= kinematic viscosity! = /*' ( = ) d (* u) /dy ! no slip condition shear stress Newtonian fluids (' viscosity depends on !emperature t ! oncentration of dissolved solutes c ! hear rate (rate of strain) s du/dy ! du/dy nonNewtonian fluids Determinants of viscosity: Temperature ... there is a huge latitudinal gradient 6  26 along the west coast 2  32 along the east coast viscosity of water at 0 = 0.0018 kg/ m s at 20 = 0.001 kg/ms at 40 = 0.0006 kg/m s viscosity of air at 0 = 0.0017 g/ m s at 20 = 0.0018 g/ms at 40 = 0.0019 g/m s Determinants of viscosity: Increases exponentially with concentration of dissolved or suspended solutes. 0 0 0.2 0.4 0.6 0.8 sugar concentration 0.2 0.4 0.6 hematocrit 0.8 b= p/(1  +,) += 0.07 exp{2.49, + 1107 exp(1.65,)/TK} A Coevolutionary Tales Nectar Feeding +! Plant! ! Pollinator! +! Butterfly and moth pollinated flowers typically produce dilute nectars: ~20% sugar concentration. Nectar feeders and blood dopers. Why are nectars dilute (low sugar concentration [S] )? What constrains hematocrit (hct)? Continuity: what goes in must come out (mass may not appear or disapear). viscosity 0 10 20 30 40 50 E gain rate S 0 10 20 30 40 50 flow rate S
0 10 20 30 40 50 Energy S Volumeout/time uout Aout
0 10 20 30 40 50 Volumein/time uin Ain uin Ain =  uout Aout S ...
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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.
 Spring '08
 daniels
 Zoology, Biomechanics

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