When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 30% of its normal value due to plaque formation, and the average pressure difference has increased by 40%, by what factor has the plaque reduced the radius of the artery?

Question

% of its normal value

Answer 1

flow rate Q2 =
v2 pi r2^2 = .3 v1 pi r1^2
v2/v1 = .3 (r1/r2)^2

.5 rho v2^2 =P2=1.4 P1=1.4*.5 rho v1^2
v2^2/v1^2 = 1.4
so
v2/v1 = 1.18
so
1.18 = .3(r1/r2)^2
r1/r2 = sqrt (1.18/.3)
= 2
so reduced to half the original radius