Graphical Description of Fluid Motion

The following are the three important concepts for visualizing or describing flow fields:

• The concept of pathline.

• The concept of streakline.

• The concept of streamline.

Pathline

Pathline may be defined as a line in the flow field describing the trajectory of a given fluid particle. From the Lagrangian view point, namely, a closed system with a fixed identifiable quantity of mass, the independent variables are the initial position, with which each particle is identified, and the time. Hence, the locus of the same particle over a time period from t0 to tn is called the pathline.

Streakline

Streakline may be defined as the instantaneous loci of all the fluid elements that have passed the point of injection at some earlier time. Consider a continuous tracer injection at a fixed point Q in space. The connection of all elements passing through the point Q over a period of time is called the streakline.

Streamlines

Streamlines are imaginary lines, in a fluid flow, drawn in such a manner that the flow velocity is always tangential to it. Flows are usually depicted graphically with the aid of streamlines. These are imaginary lines in the flow field such that the velocity at all points on these lines are always tangential. Streamlines proceeding through the periphery of an infinitesimal area at some instant of time t will form a tube called streamtube, which is useful in the study of fluid flow.

From the Eulerian viewpoint, an open system with constant control volume, all flow properties are functions of a fixed point in space and time, if the process is transient. The flow direction of various particles at time t forms streamline. The pathline, streamline and streakline are different in general but coincide in a steady flow.

Timelines

In modern fluid flow analysis, yet another graphical representation, namely timeline, is used. When a pulse input is periodically imposed on a line of tracer source placed normal to a flow, a change in the flow profile can be observed. The tracer image is generally termed timeline. Timelines are often generated in the flow field to aid the understanding of flow behavior such as the velocity and velocity gradient.

From the above mentioned graphical descriptions, it can be inferred that:

• There can be no flow through the lateral surface of the streamtube.

• An infinite number of adjacent streamtubes arranged to form a finite cross-section is often called a bundle of streamtubes.

• Streamtube is a Eulerian (or field) concept.

• Pathline is a Lagrangian (or particle) concept.

• For steady flows, the pathline, streamline and streakline are identical.