Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

# Mach Number

The Mach Number is a dimensionless value useful for analyzing fluid flow dynamics problems where compressibility is a significant factor.

The Mach Number can be expressed as

M = v / c                                  (1)

where

M = Mach number

v = fluid flow speed (m/s, ft/s)

c = speed of sound (m/s, ft/s)

Alternatively the Mach Number can be expressed with the density and the bulk modulus for elasticity as

M = v (ρ / E)1/2                            (2)

where

ρ = density of fluid (kg/m3, lb/ft3)

E = bulk modulus elasticity (N/m2(Pa), lbf/in2 (psi))

The bulk modulus elasticity has the dimension pressure and is commonly used to characterize the fluid compressibility.

The square of the Mach number is the Cauchy Number.

M2 = C                                (3)

where

C = Cauchy Number

.

### Subsonic and Supersonic speed

• If the mach number is < 1, the flow speed is lower than the speed of sound - and the speed is subsonic.
• If the mach number is ~ 1, the flow speed is approximately like the speed of sound - and the speed is transonic.
• If the mach number is > 1, the flow speed is higher than the speed of sound - and the speed is supersonic.
• If the mach number is >> 1, the flow speed is much higher than the speed of sound - and the speed is hypersonic.

### Example - Calculating an Aircraft Mach Number

An aircraft flies at speed 500 mph at an altitude of 35000 ft. The surrounding temperature is -60 oF.

The speed of sound at this altitude and temperature can be calculated

c = [k R T]1/2

= [ 1.4 (1716 ft lb/slug oR) ((-60 oF) + (460 oR)) ]1/2

= 980 ft/s

where

k = 1.4

R = 1716 (ft lb/slug oR)

The speed of the aircraft can be calculated as

v = (500 miles/hr) (5280 ft/miles) / (3600 sec/hr)

= 733 ft/sec

The Mach Number can be calculated as

M = (733 ft/s) / (980 ft/s)

= 0.75 - the aircraft is flying at subsonic speed

## Related Topics

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Air - Speed of Sound vs. Temperature

Speed of sound in air at standard atmospheric pressure with temperatures ranging -40 to 1000 °C (-40 to 1500 °F) - Imperial and SI Units.

### Bulk Modulus and Fluid Elasticities

Introduction to - and definition of - Bulk Modulus Elasticity commonly used to characterize the compressibility of fluids.

### Cauchy Number

Introduction to the Cauchy Number.

### Density vs. Specific Weight and Specific Gravity

An introduction to density, specific weight and specific gravity.

### Dimensionless Numbers

Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more.

### Solids and Metals - Speed of Sound

Speed of sound in solids and metals like aluminum, brass, concrete and more.

### Speed of Sound - Equations

Calculate the speed of sound (the sonic velocity) in gases, fluids or solids.

### Speed of Sound - Online Calculator

A free online speed of sound calculator.

### Speed of Sound vs. Elevation, Temperature and Air Pressure

Altitude and speed of sound, temperature and pressure.

### Water Hammer

Rapidly closing or opening valves - or starting stopping pumps - may cause pressure transients in pipelines known as surge or water hammers.

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.