Streak Lines

Definition: A streak line is the locus of the temporary locations of all particles that have passed though a fixed point in the flow field at any instant of time.

      Features of a Streak Line:

• While a path line refers to the identity of a fluid particle, a streak line is specified by a fixed point in the flow field.

• It is of particular interest in experimental flow visualization.

• Example:  If dye is injected into a liquid at a fixed point in the flow field, then at a later time t, the dye will indicate the end points of the path lines of particles which have passed through the injection point.

• The equation of a streak line at time t can be derived by the Lagrangian method.

If a fluid particle passes through a fixed point in course of  time t, then the Lagrangian method of description gives the equation

(7.5)

Solving for ,

(7.6)

If the positions of the particles which have passed through the fixed point are determined, then a streak line can be drawn through these points.

        Equation: The equation of the streak line at a time t is given by

(7.7)

Substituting Eq. (7.5) into Eq. (7.6) we get the final form of equation of the streak line,

(7.8)