Question

The human circulatory system delivers oxygenated blood from the lungs throughout the human body to enable the transport to and from body cells of oxygen, carbon dioxide, nutrients, hormones and blood cells. A variety of sizes of arteries and veins are required to ful?l this need.

(a) A typical heartbeat pumps 75 mL of blood over a time span of 0.36 seconds into the aorta. If under this pressure the aorta expands to a diameter of 4.2 mm, what is the average linear velocity of blood ?ow over the course of such a heartbeat? For larger arteries, friction can be neglected.

(b) As the blood ?ows to the arteries, the heartbeats become averaged so that the blood ?ows at a rate of 5.25 L/min.

i) The anterior tibeal artery delivers blood to the top of the foot, and has a diameter of 1.3 mm. What is the speed of blood ?ow in this artery, assuming that 2.5% of the blood leaving the heart enters it?

ii) If the height of our subject’s heart from the ground is 1.45 m, what is the average pressure di?erential between the blood vessel at the bottom of the foot (with the subject standing up) and the heart? Assume that blood is incompressible and has the same density as water. (Hint: Use the average blood ?ow rate in the aorta.)

(c) At the foot, the anterior tibeal artery branches into the dorsal pedis artery and the lateral tarsal artery, which branch into the dorsal metatarsal arterioles.

i) If there are 60 identical dorsal metatarsal arterioles, each with a linear ?ow velocity of 1.2m/s, ?nd the diameter of the arterioles.

ii) At this scale, viscosity becomes an important factor. Using Poiseuille’s Law, ?nd the pressure drop across an arteriole in the foot with a length of 40 mm. The viscosity of blood is 4×10?4 Pa s.

iii) What does the result from ii) imply about limitations to such narrow blood vessels as arterioles and capillaries?

Answer 1