Stream Function vs Streamlines: What's the Difference?

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Discussion Overview

The discussion centers on the differences between stream functions, streamlines, and streaklines in fluid dynamics. Participants explore the theoretical and conceptual distinctions among these terms, as well as their physical implications in flow fields.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks about the difference between stream functions and streamlines, indicating a lack of clarity on the topic.
  • Another participant expresses confusion about streaklines and their definition, suggesting a gap in available resources.
  • One participant explains that a stream function is a scalar field while streamlines are defined by an equation, noting that setting the stream function to a constant yields the equation for streamlines.
  • This participant describes streaklines as the paths followed by fluid particles, emphasizing that they depend on initial conditions rather than time, contrasting them with streamlines which are time-dependent.
  • An analogy is drawn comparing streamlines to gravitational field directions and streaklines to the actual paths of masses in that field, highlighting the dependency of streaklines on initial conditions.
  • Another participant acknowledges the explanation and indicates that understanding the difference between a function and an equation helped clarify the concepts.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the distinctions between stream functions, streamlines, and streaklines. While some explanations are appreciated, no consensus is reached on the clarity of these concepts, and confusion remains for some participants.

Contextual Notes

There are indications of missing assumptions regarding the definitions of terms and the conditions under which the concepts apply. The discussion does not resolve the complexities involved in understanding these fluid dynamics concepts.

connor415
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What is the difference between the stream function and the equation of the streamlines(if any)? cheers
 
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I also can't understand what streaklines are, and can't find anything good online :(
 
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 dependent 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.
 
Last edited:
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.
 

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