2 - = 40%) and y = 0.05 dyn/cm 2 : 1) Solve the...

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BENG 112B BIOMECHANICS S 2009 Homework #2 Due Tuesday 4/14 before class Suggested Studying and Reading: 1. Fung Chapters 3 and 6 2. Make sure you can convert the strain tensor between coordinate systems Analysis Problems: 1. In class, we discussed the N-S equation as it applies to rheology, but we neglected one critical aspect: body forces on the fluid because we stated that we were interested in the example in the context of microcirculation. Using the same example as in class, add in the one “typical” body force and resolve 1) the velocity profile, 2) the pressure distribution, 3) confirm continuity is satisfied, and 4) calculate the shear along the wall. 2. One of the constitutive equations proposed for blood is: Using our improved definition of viscosity from Thursday’s class where (J 2 ) = [( 2 J 2 ) ¼ + 2 y ½ ] 2 J 2 with set as a constant (~ 0.005 poise for whole blood with an H
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Unformatted text preview: = 40%) and y = 0.05 dyn/cm 2 : 1) Solve the stress-strain relationship for the flow field in the first problem, v(x 2 ) with all other v components equal to zero. Sketch out the relationship between 0 and 1000 sec-1 . 2) Given the values for size of the large veins, e.g. vena cava, from lecture 1, estimate the order of magnitude of the strain rate. Design Problem: Blood is a very complex fluid that requires being measured using multiple techniques to provide an accurate picture of its mechanical properties. Propose another measurement technique that utilizes the concepts of Stokes flow and assumes that blood is a homogeneous solution not a suspension. Hint : the design should include density, viscosity, and gravity . ij -p ij J 2 V kl...
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