Difficult# Dimensional Analysis: Viscosity

CHEM-7AL9EG

Viscosity can be defined as a measure of how a fluid flows. For example, honey is more viscous than water.

In general, there are two types of viscosities: dynamic (absolute) viscosity represented by the greek letter *eta* $\eta$ and kinematic viscosity represented by the greek letter *nu* $\nu$.

Dynamic viscosity can be defined by the equation:

$$F=\eta \cdot A \cdot \frac{u}{d}$$

- $F$ is force (SI unit is the Newton $\text{N} = \dfrac{\text{kg} \cdot \text{m}}{\text{s}^{2}}$)
- $\eta$ is the dynamic viscocity
- $A$ is area (SI unit is $\text{m}^{2}$)
- $u$ is velocity (SI unit is $\text{m/s}$)
- $d$ is distance (SI unit is $\text{m}$)

The kinematic viscosity is related to the dynamic viscosity by the equation:

$$\nu = \frac{\eta}{\rho}$$

...where $\rho$ is density (SI unit is $\dfrac{\text{kg}}{\text{m}^{3}}$).

Which of the following is a unit of kinematic viscosity, $\nu$?