Doppler Ultrasonic Flowmeters
rely on the Doppler effect to relate the frequency shifts of acoustic waves to the flow velocity. It usually requires some particles in the flow to reflect the signals. The rule of thumb is 25 PPM suspended solid or bubbles with diameters of 30 micron or larger for 1 MHz or higher transducers. Lower frequency transducers may require "dirtier" fluid conditions.
The Doppler formula for a sound or light source moving toward the observer at a velocity V is
Since the input signal from the transducer forms an angle with the flow direction, the velocity V should be replaced by the projected velocity V cos. The acoustic waves traveling upstream and downstream will have the observed frequencies
The difference in frequency is
since the flow velocity V is much smaller than the speed of sound c in the fluid.
By re-arranging the above equation, the flow velocity can be written as