Translation and Rotation

Introduction:
In a fluid flow, different fluid elements undergo different types of motion. Depending on the flow conditions, a fluid element in a two-dimensional flow field can experience various types of motion such as translation, deformation, rotation, or a combination of these.

Translation:
Translation refers to the movement of a fluid element from one location to another without any change in shape or orientation. In this type of motion, the fluid element moves as a whole, maintaining its original shape and orientation. It is characterized by the movement of the center of mass of the fluid element.

Deformation:
Deformation refers to the change in shape or distortion experienced by a fluid element as it moves through a flow field. This type of motion involves stretching, compression, or shearing of the fluid element. Deformation occurs due to the variations in flow velocities and pressure distribution within the fluid.

Rotation:
Rotation refers to the angular motion of a fluid element around its center of mass. In a two-dimensional flow field, rotation can occur when there is a non-zero vorticity or circulation in the flow. Vorticity is a measure of the local rotation of fluid particles within a flow field.

Explanation:
In the given question, the correct answer is option 'C', which states that the fluid element will undergo translation and rotation. This means that the fluid element will move as a whole (translation) while also experiencing angular motion around its center of mass (rotation).

In a two-dimensional flow field, translation and rotation can occur simultaneously when there is both a net force acting on the fluid element (resulting in translation) and a non-zero vorticity (resulting in rotation). The net force can be due to pressure gradients or external forces acting on the fluid element.

While translation is characterized by the movement of the center of mass, rotation is characterized by the circular motion around the center of mass. The rotation can be clockwise or counterclockwise, depending on the vorticity of the flow.

Overall, option 'C' is the correct answer because in a two-dimensional flow field, a fluid element can undergo translation and rotation simultaneously. The other options (a, b, and d) do not capture the complete motion experienced by a fluid element in such a flow field.