Viscosity

In section L1 definition of a fluid says that under the action of a shear stress a fluid continuously deforms, and the shear strain results with time due to the deformation. Viscosity is a fluid property, which determines the relationship between the fluid strain rate and the applied shear stress. It can be noted that in fluid flows, shear strain rate is considered, not shear strain as commonly used in solid mechanics. Viscosity can be inferred as a quantative measure of a fluid's resistance to the flow. For example moving an object through air requires very less force compared to water. This means that air has low viscosity than water.

Let us consider a fluid element placed between two infinite plates as shown in fig (Fig-2.1). The upper plate moves at a constant velocity  under the action of constant shear force . The shear stress, t is expressed as

where,  is the area of contact of the fluid element with the top plate. Under the action of shear force the fluid element is deformed from position ABCD at time t to position AB'C'D' at time  (fig-L2.1 ). The shear strain rate is given by

The above expression relates shear strain rate to velocity gradient along the y -axis.