Your heart pumps blood into your aorta. The maximum flow rateinto the aorta is about 500 cm3 s-1. Assume the aorta has diameter2.5 cm, that the flow is laminar, and that the blood is a Newtonianfluid with viscosity equal to that of water (1 cP). (Note theseassumptions are rather poor.)
a) Find the pressure drop per unit length along the aorta. Expressyour answer in SI units. Compare that pressure drop along a 10 cmsection of aorta with atmospheric pressure (105 Pa).
b) How much power does the heart expend just pushing blood along a10 cm section of aorta? Compare your answer with your basalmetabolic rate, about 100 W, and comment.
c) The fluid velocity in laminar pipe flow is zero at the walls ofthe pipe and maximum at the center. Sketch the velocity as afunction of distance, , from the center. Fine the velocity at thecenter. [Hint: The total volume flow rate, which you are given,equal .]
Your heart pumps blood into your aorta. The maximum flow rateinto the aorta is about 500 cm3 s-1. Assume the aorta has diameter2.5 cm, that the flow is laminar, and that the blood is a Newtonianfluid with viscosity equal to that of water (1 cP). (Note theseassumptions are rather poor.)
a) Find the pressure drop per unit length along the aorta. Expressyour answer in SI units. Compare that pressure drop along a 10 cmsection of aorta with atmospheric pressure (105 Pa).
b) How much power does the heart expend just pushing blood along a10 cm section of aorta? Compare your answer with your basalmetabolic rate, about 100 W, and comment.
c) The fluid velocity in laminar pipe flow is zero at the walls ofthe pipe and maximum at the center. Sketch the velocity as afunction of distance, , from the center. Fine the velocity at thecenter. [Hint: The total volume flow rate, which you are given,equal .]
