Viscous blood is flowing through an artery partially clogged by cholesterol. A surgeon wants to remove enough of the cholesterol to double the flow rate of blood through this artery.

Question

If the original diameter of the artery is D , what should be the new diameter (in terms of D ) to accomplish this for the same pressure gradient?

Answer 1

dV/dt = L/(R^4) for a constant pressure gradient

dV/dt = L/(1/2*D)^4 = 16L/(D^4)

2dV/dt = 16L/Dnew = 2*16L/(D^4)

Dnew = 4th root{(2*D^4)}