1) The data below refers to a steady flow of "Newtonian" blood through a long, horizontal tube. Determine:
a) Is the flow laminar or turbulent?
b) Determine the maximum velocity of the flow in a given cross-section of the tube; and
c) Calculate the shear stress at the wall.
Tube inner diameter = 3 mm
Blood: viscosity = 0.0035 Ns/m2; density = 1060 kg/m3 Mean velocity = 4 cm/s
2) Whole blood is placed in a concentric cylinder viscometer. The gap width is 1 mm and the inner cylinder radius is 30 mm. Assume that the angular velocity of the outer cylinder is 30 rev/min, and that the viscosity of the blood is µ = 0.004 Ns/m2. Determine the torque exerted on the 10 mm long (high) inner cylinder. (The blood is filled to the top of the inner cylinder.)
3) Blood flows through an aorta of 1.0 cm diameter at an average velocity of 50 cm/s. The mean pressure in this section of aorta is 100 mm Hg. The blood then enters an aneurysm with a diameter of 1.5 cm. Assuming a Young's modulus of 10,000 N/m2 and a wall thickness of 0.05 cm throughout, what is the pulse wave velocity for each of the two situations? (Note: assume blood density of 1.056 g/cc and 1 g/cm-sec2 = 7.5 x 104 mm Hg)
4) Blood flows from the left ventricle of the heart up through the ascending aorta. This system can be modeled as a narrowing tube (going from 3.1 cm to 2.7 cm diameters). The pressure in the left ventricle is 130 mm Hg, while that at the end of the ascending aorta is 123 mm Hg. The average speed of blood leaving the left ventricle is 120 cm/s. Determine the difference in height between these two locations.
5) We have a section of an artery. The vessel wall modulus of elasticity is 2.0 MPa. The artery inner diameter is 5 mm, and the wall thickness is 0.2 mm.
a. Determine the vessel compliance.
b. What would the increase in fluid pressure have to be (in mmHg) for the vessel to increase its radius by 10%?
6) List four types of replacements for arteries. List at least two issues with each of them and their 3 year patency.
7) When using solid spheres to replace red blood cells in bench testing, explain why the curve of relative viscosity versus hematocrit (percentage of cells / spheres in fluid) does not match that of red blood cells.