Measuring small air pressure gradients by a flow sensor

In this article, I discuss very small air pressure gradients: on the order of a millimeter of water (9.806 Pa, or 0.001422 psi). Conventional pressure sensors, as a rule, are not quite suitable for this purpose because their input signal spans are several orders of magnitude larger than the pressure gradients we try to measure. Thus, high gain amplification would be required with all its negative baggage, including a high level of noise.