College Physics (4th Edition)

(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) $R = \frac{8~\eta~L}{\pi~r^4}$
(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) $\Delta P = Q~\times \frac{8~\eta~L}{\pi~r^4} = I~R$ $R = \frac{8~\eta~L}{\pi~r^4}$