Blood is a very interesting fluid: a suspension of red and white blood cells and platelets in a liquid plasma. We would like to be as optimistic as Jean Poiseuille in modeling blood flow, but we know that these cells in the plasma can cause blood's viscosity to be dependent on the shear rate, that is, blood's composition can cause it to behave like a non-Newtonian fluid. Especially in regions of very low shear rate, blood's red blood cells have been shown to aggregate and form clumps that cause blood to require a certain yield stress to be applied before it flows smoothly again.
You are given the following data for an "average" person. This person's cardiac output is 5 l/min; heart rate is 60 bpm; and at a hematocrit of 40%, blood density is 1.06 g/cm3, and blood viscosity is 3.5 centiPoise (named for Jean Poiseuille, and abbreviated cP; 1 cP = 1 mPa s). Also:
Note that the vessels downstream from the heart receive only a portion of its volumetric output, due to branching of vessels. The percentages given here are ballpark estimates.
Based on these parameters, calculate the following in each of the measured vessels:
a. Pressure drop
b. Mean velocity
c. Shear rate at vessel wall
d. Reynolds number
e. Percent cross-sectional area change due to pulse pressure, assuming small strain εθθ = σθθ/E