# Summary

The Mach number is the ratio of the relative velocity of a fluid to the local speed of sound. This article provides the equation for the calculation of the Mach number and a discussion of its uses.

# Definitions

: | Mach Number | |

: | Relative Velocity of Fluid | |

: | Speed of Sound |

# Mach Number

The mach number is calculated as the ratio of the relative velocity of a fluid to the speed of sound.

There are two different scenarios for which the mach number may be applied. The first is for a object moving through a fluid, which is used in aeronautical engineering and ballistics to determine the relative speed of an aircraft, component or projectile to air. The second case is a fluid moving through or past an object, which is used in the hydraulic analysis of piping and ducting systems.

# Uses for the Mach Number

There are several practical uses for the mach number which include:

## Compressibility Assumptions

The mach number can be used to check whether it is appropriate to assume a gas is incompressible. For applications where a high degree of accuracy is not critical, calculations can be greatly simplified by assuming that a gas is incompressible. This assumption will often lead to acceptable levels of error for cases where M < 0.2-0.3.

## Choked Flow

For a gas flowing in a pipe choked flow is the point at which a decrease in the downstream pressure will not lead to an increase in flow rate. The point at which flow becomes choked is the local speed of sound. Decreasing the downstream pressure does not affect the flow rate because the pressure change can not be ‘communicated’ to the upstream fluid system, as the pressure change information can only travel at the speed of sound and hence can not influence upstream of the choke point.

Changing the upstream pressure will still have an effect on the flow rate even when flow is choked, as the pressure change will change the local speed of sound at the choke point.

## Noise Generation

Mach number can be used as a tool to assess noise generation of aircraft and equipment. Mach numbers greater than unity famously create a ‘sonic boom’, where energy accumulates into a high intensity pressure wave caused by an aircraft or projectile moving through air. The Mach number can be used to analyse individual components of aircraft, rotating machinery, or more generally any fast moving object and correlated the component to a noise generation profile. Noise generation in piping systems and through valves transporting gases can also be correlated against Mach number.

# Classification of Mach Flow Regimes

Mach flow regimes are used to classify regions which generally require different design considerations and engineering trade-offs. These are mostly applied in the aeronautical and space industries.

Regime | Mach Number |
---|---|

Subsonic | <0.8 |

Transonic | 0.8-1.2 |

Sonic | 1 |

Supersonic | 1.2-5 |

Hypersonic | 5-10 |

High-Hypersonic | >10 |

# Further Reading

- Chemical Engineering Volume 1, Sixth Edition: Fluid Flow, Heat Transfer and Mass Transfer (Coulson and Richardsons Chemical Engineering)
- Fundamentals of Aerodynamics (Anderson)
- Aerodynamics for Engineers (6th Edition)

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