Translation of a Fluid Element

Translation of a Fluid Element

      The movement of a fluid element in space has three distinct features simultaneously.

• Translation
• Rate of deformation
• Rotation. 
  

Figure 7.4 shows the picture of a pure translation in absence of rotation and deformation of a fluid element in a two-dimensional flow described by a rectangular cartesian coordinate system.

       In absence of deformation and rotation,

      a)  There will be no change in the length of the sides of the fluid element.

      b) There will be no change in the included angles made by the sides of the fluid element.

      c) The sides are displaced in parallel direction.

This is possible when the flow velocities u (the x component velocity) and v (the y component velocity) are neither a function of x nor of y, i.e., the flow field is totallyuniform.

Fig 8.1     Fluid Element in pure translation

If a component of flow velocity becomes the function of only one space coordinate along which that velocity component is defined.

        For example,

• if  u = u(x) and v = v(y), the fluid element ABCD  suffers a change in its linear dimensions along with translation
• there is no change in the included angle by the sides as shown in Fig. 7.5.

Fig 8.2  Fluid Element in Translation with Continuous Linear Deformation

         The relative displacement of point B with respect to point A per unit time in x direction is

 

        Similarly, the relative displacement of D with respect to A per unit time in y direction is