For flow velocities greater than 30% of the sonic velocity, the fluid must be treated as compressible. In compressible flow theory, one must work with the Mach number M, defined as the ratio of the flow velocity v to the sonic velocity c,
When a Pitot tube is exposed to a subsonic compressible flow (0.3 < M < 1), fluid traveling along the streamline that ends on the Pitot tube's stagnation point is continuously compressed.
If we assume that the flow decelerated and compressed from the free-stream state isentropically, the velocity-pressure relationship for the Pitot tube is,
where g is the ratio of specific heat at constant pressure to the specific heat at constant volume,
If the free-stream density rstatic is not available, then one can solve for the Mach number of the flow instead,
where is the speed of sound (i.e. sonic velocity), R is the gas constant, and T is the free-stream static temperature.