Short Answer:

Streamlines, pathlines, and streaklines are three different ways to represent the motion of fluid in flow analysis. They help engineers visualize how fluid particles move in a system. Each one describes the fluid flow from a different viewpoint.

Streamlines show the direction of fluid flow at a specific instant. Pathlines trace the actual path taken by individual particles over time. Streaklines represent the locations of all particles that passed through a common point. Though they can appear similar in steady flows, they are different in unsteady flow conditions.

Detailed Explanation:

Streamlines, pathlines, and streaklines

In fluid mechanics, especially in civil engineering fields like hydrology, irrigation, water supply, and hydraulic machinery, it is essential to understand how fluids move. To visualize this motion, we use three common flow representations: streamlines, pathlines, and streaklines. These are useful for analyzing flow in open channels, around structures, and in pipes or airflows.

Streamlines

A streamline is a line drawn in a fluid flow field where each point on the line is tangent to the velocity vector of the fluid at a particular instant. This means a streamline shows the instantaneous direction in which the fluid is moving at each location.

Streamlines do not cross each other because at any point, the fluid has only one direction of motion. They are useful for understanding the shape and direction of flow patterns at a single moment in time.

Example: In wind tunnels, smoke is used to visualize streamlines around an object like an airplane wing.

Pathlines

A pathline is the actual path or trajectory that a single fluid particle follows over time as it moves through the flow field. It shows where the particle starts, where it travels, and where it ends up.

To draw a pathline, you pick one particle and track its motion continuously over a period. It is like watching the journey of one specific drop of water as it flows through a river.

Pathlines are important in unsteady flows, where the motion of particles can change over time due to varying velocity and direction.

Streaklines

A streakline is the line formed by connecting all fluid particles that have passed through the same point in space at different times. In practical terms, it is the trace of particles that originated from the same location.

This is commonly seen when a dye is continuously injected at one spot in a fluid. The dyed fluid forms a streakline. It gives information about how particles arriving at a point behave over time and how the flow evolves.

In steady flows, streamlines, pathlines, and streaklines often appear the same. But in unsteady flows, they look different and give different types of information about the fluid motion.

Conclusion:

Streamlines, pathlines, and streaklines are three useful tools in fluid mechanics to describe and visualize fluid motion. Streamlines show the direction of flow at a moment, pathlines show the route of a single particle, and streaklines show the history of particles from a single point. Understanding their differences helps engineers analyze both steady and unsteady fluid flows effectively.