Translation and Rotation in a Two-Dimensional Flow Field

In a two-dimensional flow field in the x-y plane, a fluid element can undergo different types of motion depending on the conditions. The correct answer to this question is option 'B', which states that the fluid element can undergo both translation and rotation.

Translation refers to the movement of the fluid element as a whole in a particular direction without any change in shape. On the other hand, rotation refers to the spinning or turning of the fluid element around its center.

To understand why option 'B' is the correct answer, let's break down the different possibilities:

a) Translation Only:
If the fluid element undergoes translation only, it means that it moves without any rotation or deformation. In this case, the fluid element moves in a straight line without any change in shape.

c) Translation and Deformation:
If the fluid element undergoes translation and deformation, it means that it moves while changing its shape. This can occur when the fluid element is subjected to shear or strain forces, causing it to stretch or deform in some way.

d) Deformation Only:
If the fluid element undergoes deformation only, it means that it changes its shape without any translation or rotation. This can occur when the fluid element is subjected to forces that cause it to deform, but it remains stationary in space.

b) Translation and Rotation:
The correct answer, option 'B', states that the fluid element can undergo both translation and rotation. This means that the fluid element moves in a particular direction while also spinning or turning around its center. The combination of translation and rotation can occur in situations where there is a non-zero vorticity in the flow field. Vorticity is a measure of the local spinning or rotation of fluid particles.

In summary, in a two-dimensional flow field in the x-y plane, a fluid element can undergo translation and rotation. This combination of motion is possible when there is a non-zero vorticity in the flow field.