Theory of transit time ultrasonic flowmeters

A theory of transit time ultrasonic flowmeters for clean fluids is developed from the equations of fluid mechanics applied simultaneously to the fluid and the sound vibrations. These equations are linearized (weak sound) and use is made of the electroacoustic reciprocity theorem to give a relation between the voltages and currents at the transducer terminals and the fluid velocity. The technique of “reciprocal operation” of a transit time ultrasonic flowmeter is described and the way this technique eliminates zero drift is explained. The theory can be applied to meters with broad sound beams (which provide a better average over velocity profiles) or meters in which the wavelength of sound is not necessarily small compared with the duct diameter. Small modificaition of the sound field (due to flow) is assumed and the resulting phase (or amplitude) shift of the received signal is expressed as an integral throughout the fluid of the dot product of the fluid velocity and a weight vector defined in terms of the sound fields in the stationary fluid. Simple flowmeter designs which approach the ideal of complete immunity to velocity distribution are described.