Acoustic horizons for axially and spherically symmetric fluid flow

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary, axi-symmetric, one-dimensional (rotations around the symmetry axis are absent) flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence to either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, P proportional to p(n), we solve the equations of the fluid dynamics and show that the two possibilities are realized, respectively, for n > -I and n < - 1. The Chaplygin gas, characterized by n = - 1, corresponds to the crossover between the normal and unusual behaviour. These results are also extended to the case of spherically symmetric flow. RI Pani, Paolo/G-7412-2012 OI Pani, Paolo/0000-0003-4443-1761