Example 4

EXAMPLE 4

A fluid is rotating about the origin with angular velocity to radians per second. Find the curl and divergence of the velocity field F(x, y). As we can see from Figure 13.4.11, the velocity at a point (x, y) is F(x, y) = ω(-yi + xj) = -ωyi + ωxj

Figure 13.4.11

Then

Thus a purely rotating fluid is incompressible and its curl at every point is equal to twice the angular velocity.