Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 10%, approximately how much harder must the heart pump?
A)about 3.19 times as hard
B)about 1.80 times as hard
C)about 2.05 times as hard
D)about 1.46 times as hard
E)about 1.68 times as hard

Question

Quizplus · Accepted Answer

If the radius increases by 10%, the new radius is 1.1r. The flow rate is proportional to r^4, so the new flow rate is proportional to (1.1r)^4 = 1.4641r^4. To triple the flow rate, the heart must pump 3 times harder, so the required increase in pressure is 3/1.4641 ≈ 2.05 times.

Poiseuille's Law States That the Blood Flow Rate F