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FLUID MECHANICS - THEORY

 

In this section, the concepts of a streamline, streakline and pathline will be introduced.

     
    Streamline, Streakline and Pathline


Streamline/p>

 

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.

     

Pathline
 

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.

     
   
 
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