What is the dimension of dynamic viscosity of fluid?

Explanation:

According to Newton's law of viscosity, shear stress is directly proportional to the rate of angular deformation (shear strain) or velocity gradient across the flow.

\(τ\propto\frac{du}{dy}\)

\(τ=μ\frac{du}{dy}\)

where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear-strain).

Units of Dynamic viscosity:

\(\mu=\frac{\tau}{\frac{du}{dy}}\Rightarrow\frac{Shear\;stress}{\frac{Change\;in\;velocity}{Change\;in\;distance}}\)

\(\mu=\frac{\frac{Force}{Area}}{\frac{Length}{Time}\times\frac{1}{Length}}\Rightarrow\frac{Force\;\times\;Time}{(Length)^2}\)

\(\mu=\frac{Ns}{m^2}\)

∴ the unit of dynamic viscosity in SI unit is Ns/m2 or Pa-s.

\(\mu=\frac{Ns}{m^2}\Rightarrow \frac{kgms^{-2}\;\times\;s}{m^2}=kgm^{-1}s^{-1}\Rightarrow ML^{-1}T^{-1}\)