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 and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence of 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 ∝ ρn, we solve the equations of the fluid dynamics and show that the two possibilities are realized respectively for n > −1 and n < −1. These results are extended also to the case of spherically symmetric flow.