Dynamic viscosity $\mu$ is defined by Newton's law of viscosity:

$$\tau = \mu \frac{du}{dy} \implies \mu = \frac{\tau}{du/dy} = \frac{\text{Force} / \text{Area}}{\text{Velocity} / \text{Distance}} = \frac{[M L T^{-2}] / [L^2]}{[L T^{-1}] / [L]} = [M^1 L^{-1} T^{-1}]$$

Fundamental unit operations in fluid processing:

• Mixing is the random intermingling of two or more separate phases into a more uniform composite state.
• Kneading is a high-viscosity deformation operation used for solid doughs and plastic pastes.
• Agitation strictly refers to the induced motion of a fluid material in a specified circulatory flow pattern inside a container or tank by means of an impeller, propeller, or paddle.
• Shearing is the application of velocity gradients across fluid layers.

Dimensional derivation of dynamic viscosity:

• $\text{N}\cdot\text{s/m}$ is damping coefficient.
• From Newton's law of viscosity:
  $$\tau = \mu \frac{du}{dy} \implies \mu = \frac{\tau}{du/dy} = \frac{\text{N/m}^2}{(\text{m/s})/\text{m}} = \frac{\text{N/m}^2}{1/\text{s}} = \text{N}\cdot\text{s/m}^2$$
  This is equivalent to the Pascal-second ($\text{Pa}\cdot\text{s}$ or $\text{kg}/(\text{m}\cdot\text{s})$), the standard SI unit of dynamic viscosity.
• $\text{N/s}$ is rate of force change.
• $\text{N}\cdot\text{m}$ is torque or Joule (work/energy).