Blood flow In Example 3.3.9 we discussed Poiseuille's law of laminar flow: P -(R² – r²) 4nl v where v is the blood velocity at a distance r from the center of a blood vessel (a vein or artery) in the shape of a tube with radius R and length I, P is the pressure difference between the ends of the tube, and n is the viscosity of the blood. In very cold weather, blood vessels in the hands and feet contract. Suppose that a blood vessel with I = 1 cm, P = 1500 dynes/cm?, n = 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 center of the blood vessel at that time.

Blood flow In Example 3.3.9 we discussed Poiseuille's law of laminar flow: P -(R² – r²) 4nl v where v is the blood velocity at a distance r from the center of a blood vessel (a vein or artery) in the shape of a tube with radius R and length I, P is the pressure difference between the ends of the tube, and n is the viscosity of the blood. In very cold weather, blood vessels in the hands and feet contract. Suppose that a blood vessel with I = 1 cm, P = 1500 dynes/cm?, n = 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 center of the blood vessel at that time.