Question: A blood vessel is cylindrical with radius R and length l. The blood near the boundary moves slowly; blood at the center moves the fastest. The velocity, v, of the blood at a distance r from the center of the artery is given by
v = (P/(4ηl))(R2 - r2)
where P is the pressure difference between the ends of the blood vessel and η is the viscosity of blood.
(a) Find the rate at which the blood is flowing down the blood vessel. (Give your answer as a volume per unit time.)
(b) Show that your result agrees with Poiseuille's Law, which says that the rate at which blood is flowing down the blood vessel is proportional to the radius of the blood vessel to the fourth power.