To understand the context of the given question, we need to explore the concepts of streamline, path line, and streak line in fluid dynamics.

• Streamline: It is a line that is tangent to the velocity field at every point. Along a streamline, fluid particles have instantaneous velocity directions.
• Path line: It is the trajectory that a single fluid particle follows over time as it moves within the flow field.
• Streak line: It is formed by the locus of points of all the fluid particles that have passed through a particular point in space.

These lines represent different concepts and are generally different in fluctuating or unsteady flows. However, under certain conditions, they coincide.

The correct statement from the provided options, where streamline, path line, and streak line become identical, is when the flow is steady.

Explanation:

• In a steady flow, the flow parameters (like velocity, pressure, etc.) at any point in the fluid do not change with time. This means that the velocity field remains constant at any given point.
• Because of this constancy, every fluid particle passing through a point in a steady flow will follow the same trajectory. As a result, streamlines, path lines, and streak lines coincide with each other in steady flow conditions.
• In contrast, in an unsteady flow where flow parameters change with time, these lines differ as particles follow different paths over time and space.

Therefore, the statement "streamline, path line and streak line are identical when the flow is steady" is true and this option is the answer.

Let us evaluate the other options:

• Flow is uniform: Uniform flow implies consistent flow parameters over a given spatial region, not necessarily with respect to time. Thus, streamlines, path lines, and streak lines may differ in unsteady uniform flows.
• Flow velocities do not change steadily with time: This describes unsteady flow, where the conditions for lines to coincide are not met.
• Flow is neither steady nor uniform: This scenario will result in different streamlines, path lines, and streak lines due to varying temporal and spatial flow characteristics.

Conclusion: The correct choice is that streamlines, path lines, and streak lines are identical when the "flow is steady".