ИСТИНА

The boundary problem of the acoustic beam trajectory between two given points A and B in an arbitrary stationary three-dimensional flow of a liquid or a gas is posed. The task has a variational formulation (Fermat's principle in acoustics): Among all paths from point to point, the actual path is the one which an acoustic signal passes during the shortest time. The Fermat functional is represented as an expansion in a small Mach number up to the third order of accuracy. It is shown that the time difference between the transition of signals from point B to point A and vice versa from point A to point B is highly proportional to the flow rate and weakly depends on the detailed velocity profile. The formula for the dependence of the flow rate on the difference in time signals for a uniform flow is applicable for flow rate measuring in an arbitrary three-dimensional fluid flow. The relative error of the found formula does not exceed the square of the maximum Mach number. This allows to measure the flow rate of a liquid or gas with an arbitrary stationary subsonic velocity field.