Since you're obviously a tinkerer
Cheap will be the difficult part. A few thoughts...
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Look up "Nutating Disk" . it's the basis of your house water meter.
I see dozens of them in the brass bin at my local scrap metal yard.
I'd wager your local water company maintenance shop has a pile of old meters and they'd swap you one for a hot pizza around lunchtime.
That's a positive displacement measurement, like a pump run backwards.
..............................You know from your electrical background that a charge moving in a magnetic field feels a force
and that's the principle behind a magnetic flow meter.
This guy does a good job of explaining the principle but he failed to get one working
i think had he added a magnetic core around his pipe (near the end of the viseo) he'd have succeeded .
Beauty of that approach is your signal is already a voltage.
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Look up Rotameter,
basically a weighted float in a vertical tapered tube that's lifted by velocity of water.
It should be self cleaning because clearance gets bigger as you go up.
Tapered tubes are sold as rain gages.
View attachment 240897
but you have to measure how high is the float in the tube ...
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There's a marvelous book published by ASME titled "Fluid Meters" that's a comprehensive introduction to principles of flow measurement.
https://www.asme.org/products/books/fluid-meters-theory-application-sixth
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Who knows - you might even make a pitot instrument from the pressure transducer out of a washing machine water level sensor
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Mark Twain complained he suffered from "An excess of imagination" .
I suppose it's better than being bored...
Good Luck !old jim