MHB How to Sketch and Interpret Streamlines in a Streamfunction?

[Tranquillity]

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

 

[Dustinsfl]

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.

 

[Tranquillity]

Thank you!

 

[Tranquillity]

I have managed to plot the streamlines, any clue on the physical interpretation of the two terms?

 

[Dustinsfl]

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