First sound points in the channels

We consider barotropic irrotational stationary flows in which the local Mach number at some points is equal to one and does not exceed one everywhere. Such flows correspond to the critical freestream Mach number, which delimits purely subsonic flows and flows around with local supersonic zones. The theory of sound planes is developed (Gilbarg D., Shiffman M., 1954), which states that if an internal sound point exists in a subsonic stationary irrotational barotropic flow (local Mach number is equal to one), it lies on the sound plane, which at each point is perpendicular to the gas velocity and cannot end inside the flow. This theory does not yet provide answers to the question of the place of the first sound points in the channels. We propose along with the theorem on sound planes, to use a geometric requirement, which is not paid attention to until now. As a result, the conclusion of the location of the first sound points only on the surface of streamlined bodies can be extended to flows in a wide class of channels.