Velocity Stream Lines from Superposition of Elementary Fluid Flows

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Initially there is one locator that represents source flow at the origin, labeled "(1) = 1". The first 1 is the current number of the locator. The symbol , , or is an abbreviation for source, vortex, or doublet, respectively. The last 1 is the value of the slider "strength". Positive and negative strengths appear with yellow and green backgrounds, respectively.

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To create a new elementary flow select one of the buttons "source", "vortex", or "doublet" and place a locator. Deleting a locator reorders the numbers and the "point number" becomes 0.

The popup menu lets you: • select the locator with the current "point number" • "change flow" of the "point number" locator by the one corresponding to the active "source", "vortex", or "doublet" button • add values of the horizontal uniform velocity or/and vertical uniform velocity • change the axes scale to vary the range of the plot in steps from up to

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Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The stream functions for source, vortex, and doublet elementary flows are , , and , respectively, where is a measure of the strength of the flows.

The velocities are obtained from and . Next and are replaced by and to obtain the velocity at with strength as follows.

The source flow , from the point) or sink flow (, to the point):

Vortex flow , clockwise rotating) or , counterclockwise rotating):

Doublet flow , left through the point) or , right through the point):

Uniform flow:

This uniform flow is equivalent to the flow with velocity in the direction .

The velocity field stream lines are plotted by using superposition of the above velocities with strength located at the points .

It is interesting to compare this Demonstration with the applet given in the related links. The results are similar but the vortex positive rotation here is clockwise, while there it is counterclockwise.

See the applet on the superposition of elementary flows.



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