Flow and Temperature Profile Independence of Flow Measurements Using Long Acoustic Waves

An expansion in powers of V/c is derived for the wave number of the fundamental sound mode in a flow conduit, where V is the velocity of fluid in the conduit and c is the local sound speed. Both V and c are assumed to be independent of the longitudinal coordinates and of the time, but may have arbitrary profiles. The calculation applies to frequencies well below the cutoff frequency of the conduit, which may have an arbitrary cross-sectional shape. To lowest order, the wave number depends only on the average of the longitudinal component of V and is independent of its profile.