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# 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, $\nu$?

A

The watt, $\text{W} = \dfrac{\text{kg} \cdot \text{m}^{2}}{\text{s}^{3}}$

B

The pascal, $\text{Pa} = \dfrac{\text{kg}}{\text{m} \cdot \text{s}^{2}}$

C

The stokes, $\text{St} = \dfrac{\text{cm}^{2}}{\text{s}}$

D

The poise, $\text{P} = \dfrac{\text{g}}{\text{cm} \cdot \text{s}}$