Streamlines, streaklines, and pathlines

Streamlines, streaklines and pathlines are field lines in a fluid flow.

[1] [2] Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics: By definition, different streamlines at the same instant in a flow do not intersect, because a fluid particle cannot have two different velocities at the same point.

Streamlines provide a snapshot of some flowfield characteristics, whereas streaklines and pathlines depend on the full time-history of the flow.

Often, sequences of streamlines or streaklines at different instants, presented either in a single image or with a videostream, may provide insight to the flow and its history.

In the case of a closed curve in a steady flow, fluid that is inside a stream surface must remain forever within that same stream surface, because the streamlines are tangent to the flow velocity.

is the parametric representation of just one streamline at one moment in time.

which shows that the curves are parallel to the velocity vector.

Streamlines are calculated instantaneously, meaning that at one instance of time they are calculated throughout the fluid from the instantaneous flow velocity field.

A streamtube consists of a bundle of streamlines, much like communication cable.

The equation of motion of a fluid on a streamline for a flow in a vertical plane is:[5]

For a steady flow, the time derivative of the velocity is zero:

the curve is parallel to the flow velocity vector

, where the velocity vector is evaluated at the position of the particle

In steady flow (when the velocity vector-field does not change with time), the streamlines, pathlines, and streaklines coincide.

, further on that streamline the equations governing the flow will send it in a certain direction

As the equations that govern the flow remain the same when another particle reaches

If the flow is not steady then when the next particle reaches position

the flow would have changed and the particle will go in a different direction.

If the flow is steady, one can use streaklines to describe the streamline pattern.

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.

The center of curvature of the streamline lies in the direction of decreasing radial pressure.

The magnitude of the radial pressure gradient can be calculated directly from the density of the fluid, the curvature of the streamline and the local velocity.

Dye can be used in water, or smoke in air, in order to see streaklines, from which pathlines can be calculated.

Streaklines are identical to streamlines for steady flow.

[6] The patterns guide design modifications, aiming to reduce the drag.

The Streamline Moderne style, a 1930s and 1940s offshoot of Art Deco, brought flowing lines to architecture and design of the era.

The canonical example of a streamlined shape is a chicken egg with the blunt end facing forwards.

This shows clearly that the curvature of the front surface can be much steeper than the back of the object.

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.

The red particle moves in a flowing fluid; its pathline is traced in red; the tip of the trail of blue ink released from the origin follows the particle, but unlike the static pathline (which records the earlier motion of the dot), ink released after the red dot departs continues to move up with the flow. (This is a streakline .) The dashed lines represent contours of the velocity field ( streamlines ), showing the motion of the whole field at the same time. ( See high resolution version . )
Solid blue lines and broken grey lines represent the streamlines. The red arrows show the direction and magnitude of the flow velocity. These arrows are tangential to the streamline. The group of streamlines enclose the green curves ( and ) to form a stream surface.
The direction of magnetic field lines are streamlines represented by the alignment of iron filings sprinkled on paper placed above a bar magnet
Potential-flow streamlines achieving the Kutta condition around a NACA airfoil with upper and lower streamtubes identified.
A long-exposure photo of spark from a campfire shows the pathlines for the flow of hot air.
Example of a streakline used to visualize the flow around a car inside a wind tunnel.