I'm actually writing up a lab now where we did this to evaluate amplifier performance (EE is such a fun major!). I've never worked with flowmeters, but maybe I can help.
Basically resistors follow ohm's law. So V = IR or in words, if you put your DMM across the two terminals of the resistor, the voltage you see is the current through it times the it's rated resistance.
Their are a few tricks here. First is that the resistor will change the circuit a little. So you need to choose a resistor size that won't change the current reading too much. Generally you do this by selecting a smallish resistor, but not one too small that the reading is difficult to make.
Second, you need to actually measure the resistor. And you need to make sure that you don't heat it up too much so that its resistance changes during use.
About the devices you're measureing, they probably change their resistance to indicate the reading, right? Sort of like an RTD or thermistor. So you give them a voltage and measure the current? I've never used flowmeters, so I don't know how they work.
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