Streamline
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In fluid dynamics, a streamline is a line which is everywhere tangent to the velocity of the flow. This can be contrasted with a pathline, which is the trajectory that an imaginary infinitesimally small point would make if it followed the flow of the fluid in which it was embedded, and a streakline, which is the current location of all fluid particles that have passed through a particular spatial point in the past. In steady (time-independent) flow, the streamlines, pathlines, and streaklines coincide. A scaler function whose contours define the streamlines is known as the streamfunction.
Streamlines are frame-dependant. That is, the streamlines observed in one inertial reference frame are different from those observed in another inertial reference frame. For instance, the streamlines in the air around a aircraft wing are defined differently for the passengers in the aircraft than for an observer on the ground. When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the streamlines. In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines.
By definition, streamlines defined at a single instant in a flow do not intersect. They cannot begin or end inside the fluid.
A region bounded by streamlines is called a stream tube. Because the streamlines are tangent to the flow velocity, fluid that is inside a stream tube must remain forever within that same stream tube.
Knowledge of the streamlines can be useful in fluid dynamics. For example, Bernoulli's principle, which expresses conservation of mechanical energy, is only valid along a streamline. Also, the curvature of a streamline is an indication of the pressure change perpendicular to the streamline. The instantaneous center of curvature of a streamline is in the direction of increasing pressure, and the magnitude of the pressure gradient can be calculated from the curvature of the streamline.
Engineers often use dyes in water or smoke in air in order to see streaklines, and then use the patterns to guide their design modifications, aiming to reduce the drag. This task is known as streamlining, and the resulting design is referred to as being streamlined. Streamlined designs, like steam locomotives, streamliners and human bodies are often esthetically pleasing to the eye. The Streamline Moderne style, an 1930s and 1940s offshoot of Art Deco, brought flowing lines to architecture and design of the era.
The same terms have since become common vernacular to describe any process that smooths an operation. For instance, it is common to hear references to streamlining a business practice, or operation.
Related terms: streakline, filament line, equipotential surface
See also: drag coefficient