Chapter 2.1, Problem 83E

Blood Flow As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases (see the figure). The formula that gives v as a function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v (in cm/s) and r (in cm) is given by the function

$v(r)=18,500(0.25-r^2)0\le r\le 0.5$

1. (a) Find v(0.1) and v(0.4).
2. (b) What do your answers to part (a) tell you about the flow of blood in this artery?
3. (c) Make a table of values of v(r) for r = 0, 0.1, 0.2, 0.3, 0.4, 0.5.
4. (d) Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm.