# Viscosity

As fluid moves it is subjected to both normal stresses (pressures) and shear stresses. The shear stresses are related to the velocity gradients in the fluid. There are no shear stresses if the fluid is everywhere moving at the same speed and direction. Conversely, there are shear stresses acting within the fluid if the fluid is moving faster in some areas than in others. Viscosity is the parameter used to define the relationship between shear stresses and velocity gradients.

In a Newtonian fluid, a linear relationship exists between the shear stress and the velocity gradient. The proportionality constant in the linearrelationship is the viscosity, µ. This simple relationship can be used to describe the viscous properties of many fluids. Examples include water, oil, and air. Viscosity is very much a function of temperature. Engine oil on a cold winter morning is much more viscous than on a hot summer day.

The viscous effects of many fluids cannot be described by a linear equation. Consequently other relationships between shear stress and velocity gradients have been developed. These include rheological materials, Bingham plastics, etc.

## Learning Objectives:

How viscosity affects fluids and how it is defined.

#### Links and References

Contains a general discussion of a Newtonian fluid

Contains a discussion of the relationship between shear stress and velocity gradients for a Bingham plastic

Contains a discussion of the temperature dependency of viscosity.