Stream Function vs Streamlines: What's the Difference?

In summary, the stream function and equation of streamlines are fundamentally different, with the stream function being a function and the equation being an equation. However, they are essentially the same as the stream function can be used to define an equation for streamlines. Streaklines, on the other hand, represent the path a fluid particle will follow in a flow and are not affected by time. They only require knowledge of initial conditions and the flow field. In comparison, streamlines change with time in a steady flow.
  • #1
connor415
24
0
What is the difference between the stream function and the equation of the streamlines(if any)? cheers
 
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  • #2
I also can't understand what streaklines are, and can't find anything good online :(
 
  • #3
One is a function (ie. a scalar field, an expression) and the other is an equation, so they are fundamentally different. However when you set the stream function equal to a constant scalar you will get an equation which defines a streamline. So they are pretty much identical, physically. So the stream function is constant over streamlines, but they are not technically the same- one is a field, the other is a family of curves.Streaklines are the path a fluid drop will follow in the flow. It is a little confusing, but think of a river which gets dammed. Before it is dammed, the streamlines are straight downstream, after it is dammed, they all change because they must pass through a small hole. However, think of the streakline of a fluid particle whic is released way upstream- if the dam gets built before the particle reaches it, that streakline will pass through the hole in the dam- it will not change because it is not a function of time, only initial conditions.So an analogy would be streamlines representing the direction of a gravitational field, and streaklines representing where a mass actually goes in that field. Although the gravitational field in the solar system is always changing due to planetary motion, the streakline of, say, the Voyager probe will be only dependant on the initial conditions (and so streaklines require knowledge of the streamlines for all time). If the flow is steady, they become streamlines.

Bottom line: streamlines are lines in space depending on time. streaklines are lines in space depending only on an initial time and position, after that its path is fully described by the flow field.
 
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  • #4
yeah I had to look up the difference between a function and a equation, then it became more obvious.

Nice analogy, and really good description. Thanks.
 

Related to Stream Function vs Streamlines: What's the Difference?

1. What is a stream function and how is it different from streamlines?

A stream function is a mathematical function used to describe the motion of a fluid flow. It is a scalar quantity that is constant along a streamline. Streamlines, on the other hand, are imaginary lines that represent the direction of fluid flow at a given point. They are always parallel to the direction of the fluid velocity.

2. Can stream function and streamlines be used interchangeably?

No, stream function and streamlines are not interchangeable. Stream function is a mathematical function while streamlines are graphical representations. They serve different purposes in describing fluid flow and cannot be used interchangeably.

3. How are streamlines and stream function useful in fluid dynamics?

Streamlines and stream function are useful in fluid dynamics as they provide a visual representation of fluid flow. They can help determine the path of fluid particles, identify areas of high and low pressure, and analyze the behavior of fluid flow in different scenarios.

4. Is the stream function always constant along a streamline?

Yes, the stream function is always constant along a streamline. This is because the stream function is defined as the ratio of fluid flow rate to velocity, which remains constant along a streamline. Therefore, the value of the stream function will not change along a streamline.

5. Can stream function and streamlines be used for both laminar and turbulent flows?

Yes, stream function and streamlines can be used for both laminar and turbulent flows. However, they may be more useful in laminar flows as the fluid flow is more predictable and follows a specific path. In turbulent flows, the fluid particles may move in a more chaotic manner, making it difficult to accurately represent the flow using streamlines and stream function.

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