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One standard method of the flow material has any conductance is to use the Hall effect in what is called the electromagnetic flow meter. You run the fluid through a rectangular cross section area and put an AC magnetic field across one pair of opposite faces and electrodes on the other two faces. You measure the voltage on them with a high impedance volt meter.
Another method that only works for high speed flow is ultrasonic doppler. You TX from one sensor along the flow direction and RX the reflected signal and compare the frequencies. This can be made contactless by putting the sensors at the end of a rectangular box shape area and run the fluid in one side and out the other.
For the first question above, the flow speed has to be high in order to get a useful frequency shift. An example is that fuel flow in an truck is too slow to work, fuel flow in an airplane is fast enough to work.
These instruments are developed in industrial or university laboratories. I suspect that individuals or small businesses do not have the tools to do a good job of designing one. I do not have any documents about them.
Another type is coriolis mass flow meter. It will give the direct mass flow rate. Also it can we convert to volume becuase in the transmitter have the function to convert it.
For liquid measurement now, API already approved and it have installed a lot in the factory.
It is very popular low since the accuracy quite good, high turn down ratio and less maintenance.
I only know of some companies that sell only in large (expensive) quantities. Coors is one. Look up the key word Piezoelectric on a search engine. These are sold in large sheets with the thickness (and therefore the resonant frequency) not coltrolled very well.