power/flow/(specific heat) in SI units gives the temperature difference.
There is still an art in making a good set-up: the designer needs electronic skills and thermal at the same time. One should get between 1 and 20°C, if needed, one can adapt the power. NTC resistors change 4.5%/K, Take care that NTC sensors feel 50% of their temperature by their wires. Heat paste to the pipe, insulation around. On has to think thermally. No power should give the same temperature, no flow also. That is why the pipe needs to be horizontal. I used the principle first with air, afterwards for cyclopentane. Calorimeters with air are described in "inductors and transformers for power electronics". I did never publish the fluid one. If you want a paper could be published together (if the principle is what you need...)
I 'am agree with you. The questions posed actually include several parts: the voltage interval in volt, the correlation that connects the voltage to the measured physical variable.
At low flow I did make calorimetric ones: By preference a horizontal pipe, measure temperature left and right, with NTC resistances, heat with a given power in the middle, insulate well thermally. In set-ups it can work well.
power/flow/(specific heat) in SI units gives the temperature difference.
There is still an art in making a good set-up: the designer needs electronic skills and thermal at the same time. One should get between 1 and 20°C, if needed, one can adapt the power. NTC resistors change 4.5%/K, Take care that NTC sensors feel 50% of their temperature by their wires. Heat paste to the pipe, insulation around. On has to think thermally. No power should give the same temperature, no flow also. That is why the pipe needs to be horizontal. I used the principle first with air, afterwards for cyclopentane. Calorimeters with air are described in "inductors and transformers for power electronics". I did never publish the fluid one. If you want a paper could be published together (if the principle is what you need...)
If sensors that do not directly generate a voltage or an 'intensity' are appropriate for you then I heartily recommend the hot-wire anenometer approach advocated by Alex.
There are a number of firms that manufacture such devices, and circuit diagrams for the ingenious inventor are readily available on the web.
I have used these sensors from IST for airflow measurement with success:
Hot wire measures the local speed, where usually you need the average speed for flow. Using a hot wire is a good check if there is flow or not, but could be influenced by dirt, turbulence and so on.
...that sounded a lot like adding heat to the centre of the flow.
I understand my confusion - yours is an interesting variant - and although the heat capacity of the pipe would dampen the responsivity, for constant flows this is an interesting variant.
Well worth investigating from an Intellectual Property perspective! Mind, a calibration run is needed to 'null' the conduction path along the pipe wall.
Things can be calculated, but calorimetric things are not IP any more, but there is still an art to do it: how to inject power, how to fix NTC's. in one or two minutes it stabilises. Parasitic thermal resistance between left and right. But a thin stainless steel pipe does not conduct so much.
Air flow calorimeters need rather 10-30 minutes time constant. I used them for lamp converters, 50Hz in 4 wires out for CFL.
Though not my area of expertise, from books I woud say that a coriolis effect flowmeter could do the trick, the output of commercial ones normally give an industrial standard output (4-20 mA for example).
Attached is a link to a video from Siemens, it's in Spanish but the idea is clear.