b
${\beta=\frac{\left(\frac{F}{2 \pi r \ell}\right)}{\phi} \Rightarrow \phi=\frac{F}{2 \pi r \ell \beta}}$
$ \Rightarrow \phi = \frac{{P \times \pi {r^2}}}{{2\pi r\ell \beta }} = \frac{{Pr}}{{2\beta \ell }}$ ........$(1)$
Now rate of flow
$\Rightarrow Q=\frac{\pi \operatorname{Pr}^{4}}{8 \eta \ell}$ ...........$(2)$
$\therefore \frac{\phi}{Q}=\frac{\operatorname{Pr}}{2 \beta \ell} \times \frac{8 \eta l}{\pi p r^{4}}=\frac{4 \eta}{\pi \beta r^{3}}$
$\therefore \phi=\frac{4 \eta Q}{\pi \beta r^{3}}$