Viscosity

Viscosity is a form of internal friction. It can be measured by placing the fluid between two plates. Holding the lower plate stationary, you need to apply a force to keep the top plate moving at a constant speed parallel to the lower plate. 

Near the top plate, a friction force causes the fluid to be dragged along with the same speed. However, near the lower plate the fluid remains stationary. This sets up a velocity gradient.

Experimentally, it is found that the force per unit area which must be exerted on the top plate is proportional to this velocity gradient,

\[ \frac{F}{A} = \eta \frac{dU}{dx} .\]

$\eta$ is called viscosity.

The derivation of the $\eta$ can be found in https://www.damtp.cam.ac.uk/user/tong/kintheory/kt.pdf.

Reference:

https://www.damtp.cam.ac.uk/user/tong/kintheory/kt.pdf

https://www.thermal-engineering.org/what-is-schmidt-number-definition/