Chapter 6.5, Problem 20E

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 $v(r)=\frac{P}{4\eta l}\left(R^2-r^2\right)$ where $P$ is the pressure difference between the ends of the vessel and $\eta$ 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.