Notes of Streamline v/s Streakline v/s Pathline for GATE exam 2017

Our team of dedicated and experienced teachers have made notes of an important sub topic of this section viz, “Streamline v/s Streakline v/s Pathline“. Read it thoroughly and practise associated questions to reinstate your knowledge of the concept.

Streamline v/s Streakline v/s Pathline

Streamline 

It is an imaginary curve or line in the flow field so that tangent to the curve to any point represent the direction of instantaneous velocity at that point.

  • For unsteady flow velocity vector changes with time, the pattern of streamline also changes from instant to instant.
  • In steady flow velocity vector does not change with time, the pattern of streamline will be fixed.
  • Flow is always along streamline and there can be no flow across streamline.
  • The two streamlines can never intersect each other since the instantaneous velocity vector at a given location is always unique.

Pathline

It is a path traced by a single fluid particle at different instant of time. Pathlines are outcome of Lagrangian method and shows the path of fluid particle as a function of time

Streamlines are referred to a particular instant of time, the description of both lines involves the variation of time, since a fluid particle takes time to move from one point to another. Two path lines can intersect each other or a single pathline can itself form a loop. Different particles or even a same particle can arrive at same location at different instant of time.

A family of path lines for different particles  

  • Streamline and pathline coincides for steady flow

 

Streak line

It is a locus of position of all the particles that have passed through a fixed point at a given instant of time.

Let P be a fixed point in space through which different particles pass at different times. In an unsteady flow the velocity vector at P will change with time and hence the particles arriving at P at different times will traverse different paths like PAQ, PBR and PCS which represents path lines of particles. Let at any instant, these particles arrives at points S, R, Q. Thus S, R, Q represents the end points of the trajectories of these three particles at the instant. Therefore curve joining the points S, R, Q and fixed point P will define streak line at that instant t1.

For a steady flow, the velocity vector at any point is invariant with time and hence the pathline of different particles passing through P at different times will coincide with one another in a single curve which will indicate streakline too. Therefore in a steady flow, the pathline, streamline and streakline are identical.