Draft for Information Only 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 xyplane,
Angular Deformation In a small time interval, the angular deformations of the fluid element, for example in the xyplane.
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
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