Actually the answer is YES. Ultrasonic flow sensors which depend on piezoelectric transducers have been used for decades in precision flow measurement of gases and liquids. The principle usually requires a pair of transducers and electronics that that (1) excites a sound pulse across the fluid flow stream, and (2) receives the pulse. Doppler or time of flight principles are then used in the electronic circuits or software signal processing to determine the fluid velocity. And if you know the cross sectional area you can get the flow rate. You can read a more detailed account of ultrasonic flow sensors here.

Actually the answer is YES. Ultrasonic flow sensors which depend on piezoelectric transducers have been used for decades in precision flow measurement of gases and liquids. The principle usually requires a pair of transducers and electronics that that (1) excites a sound pulse across the fluid flow stream, and (2) receives the pulse. Doppler or time of flight principles are then used in the electronic circuits or software signal processing to determine the fluid velocity. And if you know the cross sectional area you can get the flow rate. You can read a more detailed account of ultrasonic flow sensors here.

EDIT: There is also another flow sensing technology that utilizes piezoelectric transducers - the vortex shedding flow sensor. For this technology a hydro(aero) dynamic interrupter is placed in the center of the flow stream, and is designed so that the flow streamlines separate at the back end of the interrupter - creating vortices. By placing a piezoelectric transducer at the back side of this interupter it can 'listen' to the vortex shedding. You can then count the number of vortices you hear and divide by the time interval to get a number that is proportional to the flow rate. You can learn more about vortex shedding physics here and the way Foxboro applies it to their product here.