We consider Poiscuille's law of laminar flow:
v = (P/4ηl) (R2 - r2)
where v is the blood velocity at a distance r from the centre of a blood vessel (a vein or artery) in the shape of a tube with radius R and length l, P is the pressure difference between the ends of the tube, and eta is the viscosity of the blood. In very cold weather, blood vessels in the hands and feet contract. Suppose that a blood vessel with l = 1 cm, P = 1500 dynes/cm2, eta = 0.027, and R = 0.01 cm contracts so that R'(t) = -0.0005 cm/min at a particular moment. Calculate dv/dt, the rate of change of the blood flow, at the centre of the blood vessel at that time.