Fluid Dynamics Question about streamlines help?

In summary, streamlines are imaginary lines that represent the path taken by a fluid particle in a flowing fluid. They are useful in visualizing and understanding the flow pattern and behavior of a fluid, as well as calculating important properties like velocity, pressure, and flow rate. Streamlines differ from pathlines and streaklines, which represent the actual path and past motions of fluid particles, respectively. Streamlines cannot cross each other as they represent the direction of motion of a single particle at a specific point. Streamlines can be visualized in experiments using techniques such as flow visualization, laser-induced fluorescence, and particle image velocimetry.
  • #1
bakra904
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Fluid Dynamics Question about streamlines...help!?

If the velocity field, v, of a fluid depends on x and y, v(x,y) and we know there exists some function psi(x,y) such that

vx= partial w.r.t (y) of psi
vy = -(partial w.r.t (x) of psi)

show that the curves psi(x,y) = constant, are streamlines of the flow. (a streamline is a curve which is everywhere tangent to v)
 
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See other thread. Man that's so annoying when someone posts the same question twice!
 

FAQ: Fluid Dynamics Question about streamlines help?

What are streamlines in fluid dynamics?

Streamlines are imaginary lines that represent the path taken by a fluid particle in a flowing fluid. They are defined as the tangent lines to the velocity vector of the fluid at every point.

How are streamlines useful in fluid dynamics?

Streamlines help visualize the flow pattern of a fluid and understand its behavior. They can also be used to calculate important properties such as velocity, pressure, and flow rate.

How are streamlines different from pathlines and streaklines?

Pathlines represent the actual path taken by a fluid particle, while streamlines represent the instantaneous direction of motion. Streaklines show the path of all particles that have passed through a specific point in a given time interval.

Can streamlines cross each other?

No, streamlines cannot cross each other. This is because each streamline represents the direction of motion of a single fluid particle at a specific point, and a particle cannot have two different directions of motion at the same time.

How can streamlines be visualized in experiments?

Streamlines can be visualized using techniques such as flow visualization, where particles or dye are added to the fluid to trace its motion, or by using techniques such as laser-induced fluorescence or particle image velocimetry.

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