The measuring system has a measuring transducer which produces primary signals transmitter electronics for activating the measuring transducer and for evaluating primary signals. The measuring transducer includes at least one measuring tube; at least one electro-mechanical, oscillation exciter, a first oscillation sensor. The transmitter electronics, in turn, delivers at least one driver signal for the oscillation exciter for effecting vibrations of the at least one measuring tube and generates, by means of the first primary signal and by means of the second primary signal, as well as with application of a Reynolds number, measured value representing a Reynolds number, Re, for medium flowing in the measuring transducer, a pressure difference, measured value, which represents a pressure difference occurring between two predetermined reference points in the flowing medium.