Suppose that the build-up of fatty tissue on the wall of an artery decreased the radius by 10%.By what percent would the arterial pressure difference produced by the heart have to be increased to maintain a constant blood flow?
A) 48%
B) 52%
C) 50%
D) 46%
E) 54%

Question

Quizplus · Accepted Answer

According to Poiseuille's law, the flow rate through a pipe is directly proportional to the fourth power of its radius. Thus, if the radius is decreased by 10%, the flow rate would decrease by (0.9)^4 = 0.6561 or 35.39%. To maintain a constant blood flow, the pressure difference produced by the heart would have to be increased by the reciprocal of this factor, which is 1/0.6561 or 1.523. This is equivalent to an increase of 52.3%, which is closest to option B.

Suppose That the Build-Up of Fatty Tissue on the Wall