Let be the compressibility of the fluid, i.e. . For an ideal gas at constant temperature . Hence

This is cast as a first order system

The time constant of the pitot tube is . For mm, m, at 300 K the time constant of a pitot tube exposed to flow can be calculated as 6 milliseconds. The cut-off frequency beyond which a fluctuating signal is severely attenuated can be estimated as Hz.

It is instructive to derive the pressure evolution equation in the pitot tube by suitable reduction of the Navier-Stokes equations. This discussion is left to the reader as an exercise.