How to Sketch and Interpret Streamlines in a Streamfunction?

  • MHB
  • Thread starter Tranquillity
  • Start date
In summary, the speaker is discussing a streamfunction and the task of sketching streamlines and interpreting the two terms in the function. They have managed to plot the streamlines and are seeking help with interpreting the terms. The terms represent a dipole and a freestream according to notes provided in an engineering analysis section.
  • #1
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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  • #2
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.
 
  • #3
Thank you!
 
  • #4
I have managed to plot the streamlines, any clue on the physical interpretation of the two terms?
 
  • #5
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
 

Related to How to Sketch and Interpret Streamlines in a Streamfunction?

1. What is the purpose of sketching streamlines?

The purpose of sketching streamlines is to visualize the flow of a fluid, whether it is a liquid or a gas. It helps scientists and engineers to understand the direction and magnitude of the flow in a particular system.

2. How do you sketch streamlines?

To sketch streamlines, you first need to have a velocity field, which represents the direction and magnitude of the flow at different points in the system. Then, you draw lines that are tangent to the velocity vectors at each point, creating a pattern that shows the path of the flow.

3. What do the spacing and density of streamlines represent?

The spacing and density of streamlines represent the speed and strength of the flow. Closer spacing and higher density indicate faster flow, while wider spacing and lower density indicate slower flow.

4. What are some applications of sketching streamlines?

Sketching streamlines is commonly used in fields such as fluid dynamics, aerodynamics, and hydrology. It is also used in various industries, such as designing aircrafts, predicting weather patterns, and studying ocean currents.

5. How do streamlines differ from pathlines and streaklines?

Streamlines show the instantaneous direction of the flow at a specific point, while pathlines and streaklines show the actual path that a fluid particle takes over a period of time. Pathlines are the exact path a particle takes, while streaklines are the path that a series of particles take as they pass through a specific point in the flow.

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