The only physical parameter required for the measurement principle is the well known distance between the sensors. The new system presented consists of ultrasonic sensors, transforming the natural, stochastic fluctuations of velocity, pressure and density into two signals with a delay time T, and a real-time correlator, extracting the delay time from the signals and calculating the average rate of flow of the fluid. In contrast to established flow measuring methods, no bluff bodies are necessary and electrical conductivity of the fluid is not required. In contrast to time-of-flight flow meters, a small amount of air bubbles or particles causes no signal losses and does not interrupt the measurement process. In this paper a detailed theoretical signal model describing the interaction of sound waves in random continuum and turbulent media will be presented. With this model the phase modulation of the ultrasonic waves and systematic errors can be described and some design parameters can be optimized. Measurements have been carried out with 40 and 50 mm pipe diameters for direct fluid contact and clamp-on transducers. The measurement error of the new flow meter has been found to be less than 2% from the reference value for a Reynolds number range 25 000-250 000 and, even down to a Reynolds number of 4000, it has been found to be less than 3%.