  The spacetime geometry on the equatorial slice through a Kerr black hole is
formally equivalent to the geometry felt by phonons entrained in a rotating
fluid vortex. We analyse this situation in some detail: First, we find the most
general ``acoustic geometry'' compatible with the fluid dynamic equations in a
collapsing/expanding perfect-fluid line vortex. Second, we demonstrate that
there is a suitable choice of coordinates on the equatorial slice through a
Kerr black hole that puts it into this vortex form; though it is not possible
to put the entire Kerr spacetime into perfect-fluid ``acoustic'' form. Finally,
we briefly discuss the implications of this formal equivalence; both with
respect to gaining insight into the Kerr spacetime and with respect to possible
vortex-inspired experiments.
