Fluid Flow Concepts: Streamlines, Streaklines, and Pathlines

Understanding the different lines used to describe fluid motion is crucial. Here's an analysis of the given statements:

Key Definitions

• Streamline: An imaginary line that is instantaneously tangent to the fluid velocity vector at every point.
• Pathline: The actual trajectory followed by a specific fluid particle over time.
• Streakline: The locus of all fluid particles that have passed through a specific point in space at different moments in time.

Statement Analysis

Statement 1: Streamline Definition

This statement correctly defines a streamline. The direction of the velocity vector at any point in the flow field is always tangent to the streamline passing through that point.

Result: Correct

Statement 2: Streakline vs. Pathline

This statement incorrectly defines a streakline. The description provided is actually the definition of a pathline. A streakline represents particles that have passed through a point over time, not the path of a single particle.

Result: Incorrect

Statement 3: Streakline and Streamline in Steady Flow

In steady flow, the velocity at any given point remains constant over time ($\frac{\partial \mathbf{v}}{\partial t} = 0$). Under this condition, the streakline and the streamline are identical. Every particle passing through a point follows the same path over time, and the velocity direction at that point is constant.

Result: Correct

Statement 4: Pathline and Streamline in Steady Flow

Similar to the previous point, in steady flow, velocity at a point does not change with time. Therefore, a fluid particle will always follow the same path (pathline), and the direction of velocity at any point along this path will consistently align with the tangent to that path (streamline). Hence, pathlines and streamlines coincide in steady flow.

Result: Correct

Conclusion

Based on the analysis, the correct statements are 1, 3, and 4.