When blood flows along a blood vessel, the flux f (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius r of the blood vessel. f = kr4 (this is known as poiseuille's law; we will show why it is true in section 8.4.) a partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. show that the relative change in f is about four times the relative change in r. f = kr4 ⇒ df = dr ⇒ df f = dr kr4 = 4 dr r