My current understanding is that with this technology, you can measure the flow velocity at a certain distance of the transducer, beyond the near field described in this figure.
The length Z of the near field depends on the diameter D of the emitter, and on the wavelength λ of the signal. The wavelength λ is related to the frequency f of the signal and on the speed of sound c in the water (around 1500 m/s).
For example, a 25 mm emitter operating at 3 MHz would yield a near field of 0.31 m (12 in). This example is not totally arbitrary because, as an element of motivation, I have already ordered a pair of piezoelectric transducers with these exact characteristics from this source.
I will now try to identify what kind of electronics and software will be needed to eventually get a working unit.