Kinematic viscosity only involves Length and Time (it's "kinematic"). Just like Velocity is $m/s$, Kinematic Viscosity is $m^2/s$. It describes how fast the "momentum" of the fluid spreads relative to its area.
1. Definition of Kinematic Viscosity: Kinematic viscosity is defined as the ratio of dynamic viscosity to the density of the fluid ($\rho$).
$$\nu = \frac{\mu}{\rho}$$
2. Dimensional Analysis: To find the units, we look at the SI units of the components:
• Dynamic Viscosity ($\mu$): Measured in $Pa \cdot s$ or $\frac{kg}{m \cdot s}$.
• Density ($\rho$): Measured in $\frac{kg}{m^3}$.
Calculating the resulting unit:
$$\text{Units of } \nu = \frac{kg / (m \cdot s)}{kg / m^3} = \frac{1}{m \cdot s} \times m^3 = \frac{m^2}{s}$$
3. Other Units: In the CGS system, the unit for kinematic viscosity is the
Stoke ($cm^2/s$). The SI unit is simply square meters per second ($\mathbf{m^2/s}$).