Chapter 6.5, Problem 18E

The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is

$v\left(r\right)=\frac{P}{4\eta l}\left(R^2-r^2\right)$

where P is the pressure difference between the ends of the vessel and η is the viscosity of the blood (see Example 3.7. 7). Find the average velocity (with respect to r) over the interval 0 ≤ r ≤ R. Compare the average velocity with the maximum velocity.