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We used a near-diffraction-limited flow or light-wave-interaction pipe to produce a Sagnac-interferometer-based Fresnel drag fluid flowmeter capable of detecting extremely small flow rates. An optimized design of the pipe along with the use of a state-of-the-art Sagnac interferometer results in a minimum-detectable water flow rate of 2.4 nl/s [1 drop/(5 h)]. The flowmeter's capability of measuring the water consumption by a small plant in real time has been demonstrated. We then designed an automated alignment system that finds and maintains the optimum fiber-coupling regime, which makes the applications of the Fresnel-drag-based flowmeters practical, especially if the length of the interaction pipe is long. Finally, we have applied the automatic alignment technique to an air flowmeter.