Understanding Plaque Buildup

How does the rate of blood flow through an artery depend on its radius?

$$\begin{array}{rl}F& =\int v(r)dA\\ & ={\int }_0^{R}k\left(R^2-r^2\right)\ast 2\pi rdr\\ & =2\pi k{\int }_0^R{R}^{2}r-r^{3}dr\\ & =2\pi k{\left[\frac{R^2{r}^2}{2}-\frac{r^4}{4}\right]}_0^R\\ & =2\pi k\left[\frac{R^4}{2}-\frac{R^4}{4}\right]\\ & =\pi k{R}^4\end{array}$$