Answer
(a) $\Delta P = Q~\times \frac{8~\eta~L}{\pi~r^4} = I~R$
$Q$ is the volume flow rate
$\frac{8~\eta~L}{\pi~r^4}$ is the fluid flow resistance
(b) $R = \frac{8~\eta~L}{\pi~r^4}$
Work Step by Step
(a) We can use Poiseuille's law to write an expression for the flow rate:
$Q = \frac{\pi~\Delta P~r^4}{8~\eta~L}$
$Q$ is the volume flow rate ($m^3~s^{-1}$)
$\Delta P$ is the pressure difference ($Pa$)
$r$ is the radius ($m$)
$\eta$ is the fluid viscosity
$L$ is the length of the tube ($m$)
We can find an equation for the pressure difference $\Delta P$:
$\Delta P = Q~\times \frac{8~\eta~L}{\pi~r^4} = I~R$
$Q$ is the volume flow rate
$\frac{8~\eta~L}{\pi~r^4}$ is the fluid flow resistance
(b) $\Delta P = Q~\times \frac{8~\eta~L}{\pi~r^4} = I~R$
$R = \frac{8~\eta~L}{\pi~r^4}$
