Translation with Linear Deformations
Observations from the figure:
Since u is not a function of y and v is not a function of x
This situation is referred to as translation with linear deformation.
Strain rate:
The changes in lengths along the coordinate axes per unit time per unit original lengths are defined as the components of linear deformation or strain rate in the respective directions.
Therefore, linear strain rate component in the x direction
and, linear strain rate component in y direction
Rate of Deformation in the Fluid Element
Let us consider both the velocity component u and v are functions of x and y, i.e.,
Figure 8.3 represent the above condition
Observations from the figure:
Rate of Angular deformation:
The rate of angular deformation is defined as the rate of change of angle between the linear segments AB and AD which were initially perpendicular to each other.
Fig 8.3 Fluid element in translation with simultaneous linear and angular deformation rates
From the above figure rate of angular deformation,
From the geometry
Hence,
Finally
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Translation with Linear Deformations & Rate of Deformation in the Fluid Element
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