One of Poiseuille’s laws^† says that the speed of blood V (cm/sec) flowing at a distance r (cm) from the axis of a blood vessel of radius R (cm) and length L (cm) is given by

where P (dynes/cm²) is the pressure in the vessel. Suppose a particular vessel has radius 0.0075 cm and is 1.675 cm long.

a. How fast is the blood flowing at a distance 0.004 cm from the axis of this vessel if the pressure in the vessel is 3,875 dynes/cm2?

b. Since R and L are fixed for this vessel, V is a function of P and r alone. Sketch several level curves of V(P, r). Explain what they represent.

Transcribed Image Text:

V(P, L, R, r) = 9.3P L -(R² - 1²)