# Flow Visualisation

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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:

1. Pathlines
2. Streklines
3. Streamlines
4. Timelines

## 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:

Where:
v = velocity component in y direction
u = velocity component in x direction

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).

1. Textbook p.139
2. Textbook p.140
3. Textbook p.142
4. Textbook p.139
5. Textbook p.144