Stream lines, streak lines and path lines are all identical in case of...
Uniform flow:
Uniform flow is a type of flow in which the velocity at any given point does not change with time. In other words, the flow is steady and the velocity is constant throughout the flow field.
Streamlines:
Streamlines are imaginary lines that represent the instantaneous direction of flow of a fluid at any given point. They are tangent to the velocity vector at each point. In a uniform flow, the streamlines are straight and parallel to each other. This is because the velocity is constant and does not change with time.
Streaklines:
Streaklines are the paths traced by fluid particles as they move through a flow field. They represent the history of the fluid particles and indicate the path they have followed over a certain period of time. In a uniform flow, the streaklines are also straight and parallel to each other, similar to the streamlines.
Pathlines:
Pathlines are the actual paths followed by individual fluid particles as they move through a flow field. They show the complete trajectory of a fluid particle from its initial position to its final position. In a uniform flow, the pathlines are also straight and parallel to each other, just like the streamlines and streaklines.
Explanation:
In a uniform flow, the velocity at any given point does not change with time. This means that the direction of flow is constant and does not vary with time. As a result, the streamlines, streaklines, and pathlines all coincide and are identical to each other. They are all straight and parallel to each other in a uniform flow.
However, in other types of flows, such as unsteady flow, non-uniform flow, or turbulent flow, the velocity at any given point changes with time. In such flows, the streamlines, streaklines, and pathlines do not coincide and are not identical to each other. They may curve, intersect, or diverge from each other, depending on the characteristics of the flow.
Therefore, in the case of a uniform flow where the velocity is constant and does not change with time, the streamlines, streaklines, and pathlines are all identical and represent the same flow pattern.