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 freestream state isentropically, the velocitypressure 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 freestream density r_{static} 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 freestream static temperature.
