A method for the measurement of flow rate in a pipe is proposed. The method utilizes the vibration signals that are generated using an external excitor. Three accelerometers on the surface of a pipe are used to measure these signals. Applying wave decomposition theory to the measured vibration signal, change of wave number, which is one of the results caused by flow rate change, is estimated. The change of wave number is converted into flow rate using the simple mathematical model of fluid conveying pipe. The main advantage of this method is that it does not require any sensory system inside the pipe, so that the characteristics of flow are not disturbed and the measurement position can be easily moved. All possible errors associated with the proposed measurement system are investigated. Those are due to sensor spacing, relative position of sensor with respect to boundaries, phase mismatch as well as magnitude mismatch between sensors, and measurement noise. To verify the potential of this method, experiments using water conveying steel pipe are accomplished. Finally, the estimated flow rates are within 12% error bounds.