  We impose a linearized Eulerian perturbation on a steady shallow radial
outflow of a liquid (water), whose local pressure function includes both the
hydrostatic and the Laplace pressure terms. The resulting wave equation bears
the form of an acoustic metric. A dispersion relation, extracted from the wave
equation, gives an instability due to surface tension and the cylindrical flow
symmetry. Using the dispersion relation, we also derive three known relations
that scale the radius of the circular hydraulic jump in the outflow. The first
two relations are scaled by viscosity and gravity, with a capillarity-dependent
crossover to the third relation, which is scaled by viscosity and surface
tension. The perturbation as a high-frequency travelling acoustic wave,
propagating radially inward against the bulk outflow, is blocked just outside
the circular hydraulic jump. The amplitude of the wave also diverges here
because of a singularity. The blocking is associated with surface tension,
which renders the circular hydraulic jump an acoustic white hole.
