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7.2: Stationary Flows

Last updated

May 3, 2023
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- 7.1: Velocity Fields
- 7.3: Physical Assumptions and Mathematical Consequences

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If the velocity field is unchanging in time we call the flow a stationary flow. In this case, we can drop $t$ as an argument and write:

$F(x, y) = (u(x, y), v(x, y)) \nonumber$

Here are a few examples. These pictures show the streamlines from similar figures in topic 5. We’ve added arrows to indicate the direction of flow.

Example $\PageIndex{1}$ : Uniform Flow

$F = (1, 0)$ .

001 - (Example 7.3.1).svg — Figure $\PageIndex{1}$ : Velocity field of a uniform flow. (CC BY-NC; Ümit Kaya)

Example $\PageIndex{2}$ : Eddies (Vortexes)

$F = (-y/r^2, x/r^2)$

002 - (Example 7.3.2).svg — Figure $\PageIndex{2}$ : Velocity field of an eddy (vortex). (CC BY-NC; Ümit Kaya)

Example $\PageIndex{3}$ : Source

$F = (x/r^2, y/r^2)$

003 - (Example 7.3.3).svg — Figure $\PageIndex{3}$ : Velocity field of a source. (CC BY-NC; Ümit Kaya)

Example 7.2.1\PageIndex{1}: Uniform Flow

Example 7.2.2\PageIndex{2}: Eddies (Vortexes)

Example 7.2.3\PageIndex{3}: Source

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Example $\PageIndex{1}$ : Uniform Flow

Example $\PageIndex{2}$ : Eddies (Vortexes)

Example $\PageIndex{3}$ : Source