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In the study of fluid mechanics, streamlines are often drawn to visualize
the flow field. At every point in the flow field, a streamline is tangent
to the velocity vector. That is, for 2D flow in Cartesian coordinates,
The above equation can be integrated to give the equation of a streamline once the velocity field (i.e., u and v) is known. For every streamline, there is a stream function (Ψ) associated with it. The definition of the stream function will be covered in differential Conservation of Mass section.
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A streakline consists of all fluid particles
that have previously passed through a specified point. This is essentially
the same as injecting dye or smoke continuosly at a given location
and observing how the dye or smoke moves along with the fluid
motion. This is a technique that is often used in experiments to visualize
the flow field.
On the other hand, the actual path that a single fluid particle takes
is referred to as the pathline, i.e., it is the trajectory of a
particular fluid particle. This is referred to as the Lagrangian viewpoint of the flow field. Experimentally,
it can be achieved by tagging a fluid particle and tracing its motion
throughout the flow field.
In general, a streamline, streakline and pathline are not the same; however, they coincide when the flow is steady.