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

(a) Find the average velocity $v_{ave}$ (with respect to $r$) over the interval $0 \le r \le R.$

Note: Your answer may contain $\eta$, which is not a symbol on your keyboard. In your answer, use a lower-case "n" in its place.

Average velocity =

(b) Compare the average velocity $v_{ave}$ with the maximum velocity $V$. How are they related? Answer this by writing an equation that gives $v_{ave}$ as a function of the maximum velocity $V$.

$v_{ave} =$