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The physical principles of the ultrasound cross-correlation flow meter are described quantitatively by means of an approach based on system analysis. We extend an earlier theoretical model of Shu (1987 PhD Thesis Universität Karlsruhe) by accounting for additional characteristics of the turbulent pipe flow and making use of characteristic turbulence parameters. The velocity obtained by cross-correlation of the phase-modulated ultrasound signals can be predicted with the theoretical model as a function of the Reynolds number. These theoretical predictions agree favourably with experimental results. It is shown that the velocity determined by cross-correlation is nearly the 'modal value' of the turbulent velocity profile and, thereby, higher than the bulk velocity in the pipe. The investigations include studies of the influence of a number of parameters that can be varied in a practical set-up. It is shown that a calibration of the system, as it is done in practice, is only valid for a specific set of values of these parameters and restricted to fully developed flow in the pipe.

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