Hence

as given earlier. In compressible flows with Mach number M , Bernoulli equation is written as

The integral can be evaluated by assuming ideal gas behaviour and a reversible adiabatic process that brings the fluid particles to rest at point 0 (i.e., = constant). It can be shown that

where is the ratio of specific heats, is the speed of sound equal to , is the specific gas constant (=287 J/kg K for air) and the absolute temperature of the fluid at point 1. Pressure is the stagnation pressure recorded by the pitot tube.