Fluid Motion

The fluidity property of fluid makes the motion of fluid very complex. The velocity variation of each fluid particle during fluid flow within the velocity field caused by forces results fluid element deformation. The deformation of fluid is similar to that of solid except fluid deforms continuously and therefore express in terms of rate of deformation or strain rate. Types of fluid motion and deformation are translation, linear deformation, rotation, and angular deformation.

Linear Translation

The linear translation of a fluid element in a small time interval with same field velocity along the flow direction, for example in xy plane

Linear Deformation

The linear deformation of a fluid element in a small time interval with field velocity gradient along the flow direction, for example in xy plane

Linear Strain Rate

The linear strain rate or the rate of change of length per unit length along one of the flow direction can be expressed as

Let , the volumetric strain rate or the bulk strain rate is then

Angular Rotation

When there is a cross flow velocity gradient along the flow, the fluid element will rotate, for example in the xy-plane,

Angular Deformation

In a small time interval, the angular deformations of the fluid element, for example in the xy-plane.

Therefore for small angles,

and

Angular Strain Rate

The angular strain rate or the rate of shear strain by definition can be expressed as

and in terms of strain rate tensor