Are streamlines parallel in inviscid and irrotational flow

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Discussion Overview

The discussion revolves around the nature of fluid streamlines in the context of irrotational and viscous flows. Participants explore whether streamlines can be parallel in such flows and the implications of flow characteristics on streamline behavior.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether streamlines in an irrotational but viscous flow can be parallel, or if the flow must be both irrotational and inviscid for that to occur.
  • Another participant asserts that streamlines are always parallel to the local velocity, but they do not need to be parallel to each other, highlighting that they can get closer together in accelerating flow.
  • A repeated point emphasizes that streamlines cannot cross and are defined as lines parallel to the local velocity at each point.
  • A participant seeks clarification on the conditions under which streamlines of individual fluid elements would be parallel.
  • There is a distinction made between streamlines and pathlines, with a participant noting that for steady flow, pathlines are identical to streamlines.

Areas of Agreement / Disagreement

Participants express differing views on the conditions necessary for streamlines to be parallel, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are unresolved assumptions regarding the definitions of streamlines and pathlines, as well as the implications of flow characteristics on their behavior.

charlies1902
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Are fluid streamlines in an irrotational, but viscous, flow parallel? Or does the flow need to be both irrotational and inviscid?
 
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Streamlines are always parallel to the local velocity. They don't have to be parallel to each other (though they can never cross). For example, if the flow accelerates in a region, streamlines will get closer together, which couldn't happen if they had to be parallel.
 
boneh3ad said:
Streamlines are always parallel to the local velocity. They don't have to be parallel to each other (though they can never cross). For example, if the flow accelerates in a region, streamlines will get closer together, which couldn't happen if they had to be parallel.
Oh I see. But if we are strictly talking about streamlines of individual fluid elements, in which case would the streamlines be parallel?
 
charlies1902 said:
Oh I see. But if we are strictly talking about streamlines of individual fluid elements, in which case would the streamlines be parallel?

I am not even sure what you mean by that. Streamlines are defined as lines that are parallel to the local velocity at each point along their paths. If you are talking about the path an individual particle would take through a flow, that is generally called a pathline, and for a steady flow, is identical to the streamlines.
 

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