# Flow Fundamentals (Streamline – Streakline – Pathline – Stream Tube)

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#### Flow Fundamentals (Streamline – Streakline – Pathline – Stream Tube)

Here we will explain the flow fundamentals principles needed whenever fluid movements are studied. Fluid Mechanics could be so harsh, especially when we are dealing with these flow fundamentals. If you want to identify the differences between Lagrangian method and Eulerian method, this post will help you.

## Flow Fundamentals : Lagrangian Method VS Eulerian Method

There are two methods for studying the movement of flow. One is a method which follows any arbitrary particle with its kaleidoscopic changes in velocity and acceleration. This is called the Lagrangian method. The other is a method by which, rather than following any particular fluid particle, changes in velocity and pressure are studied at fixed positions in space x, y, z and at time t. This method is called the Eulerian method. Nowadays the latter method is more common and effective in most cases.

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### Streamline - Streakline - Pathline

A curve formed by the velocity vectors of each fluid particle at a certain time is called a streamline. In other words, the curve where the tangent at each point indicates the direction of fluid at that point is a streamline. Floating aluminum powder on the surface of flowing water and then taking a photograph, gives the flow trace of the powder as shown in the following figure. A streamline is obtained by drawing a curve following this flow trace. From the definition of a streamline, since the velocity vector has no normal component, there is no flow which crosses the streamline. Considering two-dimensional flow, since the gradient of the streamline is dy/dx, and putting the velocity in the x and y directions as u and v respectively, the following equation of the streamline is obtained :

$\frac{{dx}}{u} = \frac{{dy}}{v}$

Whenever streamlines around a body are observed, they vary according to the relative relationship between the observer and the body. By moving both a cylinder and a camera placed in a water tank at the same time, it is possible to observe relative streamlines. On the other hand, by moving just the cylinder, absolute streamlines are observed. In addition, the lines which show streams include the streak line and the path line. By the streak line is meant the line formed by a series of fluid particles which pass a certain point in the stream one after another. As shown in the figure, by instantaneously catching the lines by injecting dye into the flow through the tip of a thin tube, the streak lines showing the turbulent flow can be observed. On the other hand, by the path line is meant the path of one particular particle starting from one particular point in the stream. As shown in the figure, by recording on movie or video film a balloon released in the air, the path line can be observed.

Streamline is the curve where the tangent at each point indicates the direction of fluid at that point at a certain time. Streak line is the line formed by a series of fluid particles which pass a certain point in the stream one after another. Path line is the path of one particular particle starting from one particular point in the stream. In the case of steady flow, the above three kinds of lines all coincide.

### Stream Tubes

By taking a given closed curve in a flow and drawing the streamlines passing all points on the curve, a tube can be formulated as shown in the following figure. This tube is called a stream tube. Since no fluid comes in or goes out through the stream tube wall, the fluid is regarded as being similar to a fluid flowing in a solid tube. This assumption is convenient for studying a fluid in steady motion.

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