Answer
Viscosity has SI units of pascal-seconds.
Work Step by Step
Poiseuille's law:
$Q = \frac{\pi~P~r^4}{8~\eta~L}$
$Q$ is the flow rate ($m^3~s^{-1}$)
$P$ is the pressure ($Pa$)
$r$ is the radius ($m$)
$\eta$ is the fluid viscosity
$L$ is the length of the tube ($m$)
We can rearrange the equation:
$\eta = \frac{\pi~P~r^4}{8~Q~L}$
We can replace the variables on the right side of the equation with their units:
$\frac{(Pa)~(m)^4}{(m^3~s^{-1})~(m)} = Pa \cdot s$
Viscosity has SI units of pascal-seconds.
