Neighboring layers of a moving fluid can slide past one another at different speeds. Viscosity measures the fluid's resistance to this relative motion.

For a Newtonian fluid in simple shear, Newton's law of viscosity is

$$\tau=\mu\frac{du}{dy},$$

where $\tau$ is shear stress, $du/dy$ is the velocity gradient and $\mu$ is the dynamic viscosity.

Velocity gradients create shear

If all neighboring layers move at the same velocity, there is no velocity gradient and this viscous shear stress vanishes. A larger gradient produces a larger shear stress for the same fluid.

Dynamic and kinematic viscosity

The kinematic viscosity is

$$\nu=\frac{\mu}{\rho}.$$

It combines viscous resistance with density and appears naturally in many flow-scaling relations.

Temperature dependence

Liquid viscosity generally decreases as temperature rises, while gas viscosity generally increases. The molecular mechanisms producing viscosity differ between the two cases.