How to Sketch and Interpret Streamlines in a Streamfunction?

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Discussion Overview

The discussion revolves around the sketching and interpretation of streamlines derived from a given streamfunction \(\psi(r,\,\theta) = U\left(r-\frac{a^2}{r}\right)\sin{\theta}\). Participants are exploring both the graphical representation of the streamlines and the physical significance of the terms within the streamfunction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests assistance in sketching the streamlines and interpreting the terms of the streamfunction.
  • Another participant suggests rewriting the streamfunction in terms of \(x\) and \(y\) and using Mathematica's streamplot feature for visualization.
  • A participant indicates they have successfully plotted the streamlines and seeks clarification on the physical interpretation of the two terms in the streamfunction.
  • Another participant mentions that one of the terms represents a dipole, implying a specific physical interpretation, but does not elaborate further.

Areas of Agreement / Disagreement

The discussion shows some participants agreeing on the need for physical interpretation of the streamfunction terms, while there is no consensus on the interpretations themselves, and multiple views are presented without resolution.

Contextual Notes

Participants reference external materials, such as Engineering Analysis notes, for additional context and resources related to the streamfunction and its interpretation.

Tranquillity
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Hello guys!

I have the streamfunction \(\psi(r,\,\theta) = U\left(r-\frac{a^2}{r}\right)\sin{\theta}\), \(a\) is a positive constant and I have to sketch the streamlines and also interpret the two terms in the streamfunction!

Any clue on how to do that?

Thank you very much

Kindest regards
 
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Tranquillity said:
Hello guys!

I have the streamfunction \(\psi(r,\,\theta) = U\left(r-\frac{a^2}{r}\right)\sin{\theta}\), \(a\) is a positive constant and I have to sketch the streamlines and also interpret the two terms in the streamfunction!

Any clue on how to do that?

Thank you very much

Kindest regards

Re-write in terms on x and y and use the streamplot feature in Mathematica. Refer to the math notes section Engineering Analysis notes for downloadable Mathematica notebooks that make these plots.
 
Thank you!
 
I have managed to plot the streamlines, any clue on the physical interpretation of the two terms?
 
Tranquillity said:
I have managed to plot the streamlines, any clue on the physical interpretation of the two terms?

Did you read the notes on those sections? One is a dipole
 

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