Mach Number (supersonic, calculated from Pitot Tube Pressure)

Description

In fluid mechanics, Mach number (M or Ma) is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local speed of sound.
Mach number varies by the composition of the surrounding medium and also by local conditions, especially temperature and pressure. The Mach number can be used to determine if a flow can be treated as an incompressible flow. If M < 0.2–0.3 and the flow is (quasi) steady and isothermal, compressibility effects will be small and a simplified incompressible flow model can be used.

At altitude, for reasons explained, Mach number is a function of temperature. Aircraft flight instruments, however, operate using pressure differential to compute Mach number, not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the stagnation pressure sensed by a Pitot tube is dependent on altitude as well as speed.

Assuming air to be an ideal gas, the formula to compute Mach number in a supersonic compressible flow can be found from the Rayleigh Supersonic Pitot equation using parameters for air, as shown here.

Related formulas

Variables

Mmach number (dimensionless)
qCimpact pressure (dynamic pressure) (pascal)
pstatic pressure (pascal)