Path Line

Path line and Stream line

Path Line

Definition :

  Path line is the line traced by a single fluid particle as it moves over a period of time.

Fig. 2.1   Path lines

A family of path lines represents the trajectories of different particles, say, P1, P 2, P3, etc. (Fig. 2.1)

• Path line shows the direction of velocity of the same fluid particle at successive instants of time.

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Stream Line

Definition :
  
  A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector.

• Stream line shows the direction of velocity of a number of fluid particles at the same instant of time. Path line shows the direction of velocity of the same fluid particle at successive instants of time.

Distinguish between stream line and path line

Path Line	Stream Line
This refers to a path followed by a fluid particle over a period of time.	This is an imaginary curve in a flow field for a fixed instant of time, tangent to which gives the instantaneous velocity at that point .
Two path lines can intersect each other as or a single path line can form a loop as different particles or even same particle can arrive at the same point at different instants of time.	Two stream lines can never intersect each other, as the instantaneous velocity vector at any given point is unique.

Note: In a steady flow path lines are identical to streamlines as the Eulerian and Lagrangian versions become the same.

Stream tube:

A bundle of neighboring streamlines may be imagined to form a passage through which the fluid flows. This passage is known as a stream-tube.

Properties of Stream tube:

1. The stream-tube is bounded on all sides by streamlines.

2. Fluid velocity does not exist across a streamline, no fluid may enter or leave a stream-tube except through its ends.

3. The entire flow in a flow field may be imagined to be composed of flows through stream-tubes arranged in some arbitrary positions.



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Can the path line and a streamline cross each other at right angles?
A fluid particle always moves tangent to the streamline. In steady flow, the path lines and streamlines are identical. In unsteady flow, a fluid particle follows one stream line at one instant and another at the next instant and so on, so that the path line have no resemblance to any given instantaneous streamline.