7.1: Velocity Fields
- Page ID
- 6509
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Suppose we have water flowing in a region \(A\) of the plane. Then at every point \((x, y)\) in \(A\) the water has a velocity. In general, this velocity will change with time. We’ll let \(F\) stand for the velocity vector field and we can write
\[F(x, y, t) = (u(x, y, t), v(x, y, t)). \nonumber \]
The arguments \((x, y, t)\) indicate that the velocity depends on these three variables. In general, we will shorten the name to velocity field (Figure \(\PageIndex{1}\)).
A dynamic beautiful and mesmerizing example of a velocity field is at http://hint.fm/wind/index.html. This shows the current velocity of the wind at all points in the continental U.S.