# 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. Here, the four most important flow visualisations are explained. Briefly, they are:

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

## Contents

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

## Pathlines

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

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

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

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.