The velocity potential associated with the free vortex can then be determined
as follows:
Since V_{r} = ∂φ/∂r, the velocity potential is not a function of r, and f(r) reduces to an
arbitrary constant. For simplicity, set f(r) = 0 (the value of
an individual velocity potential is irrelevant) to yield
φ = Kθ
Note that when a flow is referred to as irrotational, it simply implies
that the individual fluid elements do not rotate. Although
the fluid elements of the given free vortex follow a circular path, it
is still irrotational flow. |