Question

do the second prob pic

Consider a medical device where blood is circulated in the annular space between two coaxial cylinders (Figure 1). The inner cylinder (radius cylinder (radius R) is rotating with constant anacibeNewtonian fluid (density o. are infinitely long, and that blood behaves as an tncompcessiole viscosity . Ignore the effect of gravity. whereas the outer velocity oAssume that the cylinders 1a. Write a conservation equations appropriate to determine the fluid velocity profile insido the annular gap, along with a sufficient number of boundary conditions. Justify your assumptions. (10 points) 1b. Integrate the conservation equation to find an expression for the flow velocity, without calculating the constants of integration (i.e. leave them as Ch and Ca). (S points) FLUID Consider a device with the same geometry as in Problem 1. In this case cylind plane of thepage inFigure!) with a constant velocity U트し, mus. Again, the inner cylinder (radius Ro 2.0 em) is not moving. Under these conditions, the velocity profile in the annular gap can be described by the following equation: er (radius RI , though, the outer 35 cm) is not rotating, but moving along its axis (perpendicular to the In(r/R) Write a MATLAB/Octave script to create a surface plot of the velocity profile v, at any cross-section of the annular gap (i.e. the gray area in Figure 1). (10 points) Tip I: in MATLAB/Octave, the function for the natural logarithm is "log". Tip 2: the velocity profile above is given in cylindrical coordinates, while the function surf(x.y.vz)" (surface plot) requires Cartesian coordinates. Use the trigonometric relations between r,θ and x), as covered in class.

Answer 1

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