1.

Segment V4.1: Velocity Field
(Related to Textbook Section 4.1 - The Velocity Field)

A field representation is often used to describe flows. In doing so, the flow parameters are specified as functions of the spatial coordinates and time. The velocity field describes a flow by giving the point-bypoint fluid velocity throughout the flow field.

The calculated velocity field in a shipping channel is shown as the tide comes in and goes out. The fluid speed is given by the length and color of the arrows. The instantaneous flow direction is indicated by the direction that the velocity arrows point. (Video courtesy of Danish Hydraulic Institute.)

2.

Segment V4.2: Flow Past a Wing
(Related to Textbook Section 4.1.2 - One-, Two-, and Three-Dimensional Flows)

Most flows involve complex, threedimensional, unsteady conditions. The flow past an airplane wing provides an example of these phenomena.

The flow generated by an airplane is made visible by flying a model Airbus airplane through two plumes of smoke. The complex, unsteady, three-dimensional swirling motion generated at the wing tips (called trailing vorticies) is clearly visible. An understanding of this motion is needed to ensure safe flying conditions, especially during landing and take-off operations where it can be dangerous for an airplane to fly into the preceding airplane's trailing vorticies. (Video copyright ONERA.)

3.

Segment V4.3: Flow Types
(Related to Textbook Section 4.1.3 - Steady and Unsteady Flows)

Among the many ways that flows can be categorized are: a) steady or unsteady, b) laminar or turbulent. Which type of flow occurs for a given situation depends on numerous parameters that affect the flow.

The low speed flow of water from a small nozzle is steady and laminar. Unless the flow is disturbed (by poking it with a pencil, for example), it is not obvious that the fluid is moving. On the other hand, the flow within a clothes washer is highly unsteady and turbulent. Such motion is needed to produce the desired cleaning action.

4.
 

Segment V4.4: Jupiter Red Spot
(Related to Textbook Section 4.1.4 - Streamlines, Streaklines, and Pathlines)

Flow visualization experiments can be quite helpful in understanding various flow phenomena. One common visualization technique involves the observation of a tracer material (such as dye or smoke) that has been injected into the flow field.

The giant red spot on Jupiter (approximately 7 times longer than the diameter of the Earth) is a huge vortex ("swirl") in the atmosphere of Jupiter, similar in some ways to a hurricane on Earth. The turbulent, eddying flow in Jupiter's atmosphere is made visible by the color contrast in the atmospheric material.

5.

Segment V4.5: Streamlines
(Related to Textbook Section 4.1.4 - Streamlines, Streaklines, and Pathlines)

A streamline is a line that is everywhere tangent to the velocity field. For steady flow, the streamlines are fixed lines in a flow field which show the paths the fluid particles follow.

Streamlines created by injecting dye into water flowing steadily around a series of cylinders reveal the complex flow pattern around the cylinders. Also, as shown for flow around a series of airfoil shapes, the stagnation streamline and corresponding stagnation point can be easily observed (see top airfoil). Stagnation points on the other airfoils could be located by adjusting the upstream position of the incoming streamlines.

6.

Segment V4.6: Pathlines
(Related to Textbook Section 4.1.4 - Streamlines, Streaklines, and Pathlines)

A pathline is the line traced out by a given particle as it flows from one point to another. The lawn sprinkler rotates because the nozzle at the end of each arm points "backwards".

This rotation give the water a "forward" component. As a result, water particles leave the end of each spray arm in a nearly radial direction. Once the water exits the spray arm there is no external force to change its velocity (neglecting aerodynamic drag and gravity). Thus, the pathlines are essentially straight radial lines, whereas the shape of the water streams (which are not pathlines) is a complex spiral about the axis of rotation.