BE_110_HW_7

BE_110_HW_7 - . Design a technique to non-invasively...

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BE 110 An Introduction to Biomechanics Fall 2005 Homework Assignment #7 Due Tuesday 11/22/05, 8AM before class 1. Reading assignment In addition to the strains we have discussed in class there are other measures of deformation. One of the is the displacement gradients and the Finger strain tensors. See section 5.10. 2. Practice Problems Derive the infinitesimal strain components in polar coordinates. See section 5.8. 3. *Analysis Problem . The motion of an incompressible fluid can be described by a stream function ψ . Stream functions are useful in two-dimensional and in axisymmetric flows fields. Let u(x,y) and v(x,y) be the velocity components such that u = ∂ψ y and v = x and w = 0. Sketch the velocities u,v and streamlines ψ = constant for the following functions ψ (x,y): ψ = y; ψ = x 2 + y 2 ; ψ = - sin θ/ r; ψ = - r sin θ where θ and r are radial angle and radius of a polar coordinate system. 4. *Design Problem
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Unformatted text preview: . Design a technique to non-invasively measure the velocity in a blood vessel. Consider a blood vessel close to the surface of the skin (e.g. on the back of your hand). There are different levels of details that can be measured: the average velocity and the velocity profile. Consider both possibilities. Describe in detail the method of approach, a calibration of the measurement, and the limitations of the approach. How would you determine the smallest size of blood vessel in which you can measure the velocity? Note: There is a need to significantly improve and also simplify the techniques to measure the velocity in human blood vessels, so that the measurement becomes more accessible especially to patients with high risk for cardiovascular complications. - Our Plans: Next week we will speak about strain rates and constitutive equations. * To be turned in for grading...
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