# Flow Visualisation

While mathematical analysis allows for accurate understanding, it is very useful to be able to visualise flows in order to understand the whole picture^{[1]}. Here, the four most important flow visualisations are explained. Briefly, they are:

- Pathlines
- Streklines
- Streamlines
- Timelines

## Contents |

## Textbook Readings

Cengel and Cimbala, Fluid Mechanics: Fundamentals and Applications, (2nd ed, Singapore, McGraw Hill Education, 2010), pp. 139-145.

## Pathlines

^{[2]}A pathline is the path travelled by a single fluid particle over a period of time. It is essentially the same as the position vector of a single particle. Hence it's equation is stated as:

## Streaklines

^{[3]}A streaklines is the locus of fluid particles that have passed sequentially through a point in the flow. This is the **most commonly** used flow path in experiments. It is usually seen by injecting smoke or dye into a flow and following it. Mathematically, it can be stated as:

## Streamlines

^{[4]}A streamline is a curve that is everywhere tangent to the instantaneous loca velocity vector. In other words it is the instantaneous direction of fluid motion. In the x-y plane, it can be shown that a streamline is mathematically given by:

*Note: under steady flow, pathlines, streaklines and streamlines are equivalent*

## Timelines

^{[5]}A timeline is a set of adjacent fluid particles that were marked at the same instant in time. This type of flow helps to determine the uniformity of the flow.

## References

"Textbook" refers to Cengel and Cimbala, Fluid Mechanics: Fundamentals and Applications, (2nd ed, Singapore, McGraw Hill Education, 2010).