The irony here is that aeronautical engineers build models of air flow based on a misapplication of data from pressure taps fed into the Bernoulli Equation to calculate airspeed at the surface of the wing at various points, claiming without any proof whatsoever that the results are accurate, while pilots use a device that does not use the Bernoulli Effect at all to accurately measure airspeed, which is critical to their survival.
Air has mass. Mass implies momentum. Changes in momentum constitute acceleration. When a closed tube (a pitot tube) is thrust into an airstream, the air that goes into that tube is quickly accelerated into the direction of the pitot tube. That acceleration creates weight, measured by the aneroid wafer. The greater the differential between the speed of the ambient air and the pitot tube, the more acceleration, and the more weight.
That weight compresses the air, so yes, it is denser in the tube than it is in the ambient air. That air would decompress out through the mouth of the tube to match the pressure of the ambient air, except that this is disallowed by the acceleration of more air striking the mouth of the tube.
The constant stream of oncoming air maintains the pressure in the tube, so as the relative speed of the air and tube change, so does the pressure, and so does the pressure reading, which is translated into airspeed.
The Bernoulli Equation was invented to measure blood flow in a blood vessel in the 1700s. It assumed an incompressible fluid flowing through a vessel with parallel walls, neither converging nor diverging.
Einstein ignorantly developed the "Longer Path" theory of lift generation of wings based on a misapplication of the Bernoulli Effect. Orville Wright argued that he was wrong, and Einstein accepted that he was ignorant and should not have posited the theory, but because of hero worship for Einstein's intellectual prowess, engineers really, REALLY want to use the Bernoulli Equation to measure airspeed.
Pressure taps measure pressure. They do not measure airspeed. Models of airspeed at the surface of wings based on data from pressure taps are deeply flawed, and yet they dominate aeronautics.
If the Bernoulli Equation could give you an accurate airspeed, then airplanes would use a device different from a pitot tube with an aneroid wafer to accurately measure airspeed. Engineers proclaim that air is "incompressible" at subsonic speeds, and yet here, inside the pitot tube is compressed air. If it wasn't compressed, the instrument would not measure airspeed.
And yet, it does.