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.

Mach Number

Introduction to the Mach Number

Sponsored Links

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

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Share

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.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Topics

Unit Converters

Temperature

oC
oF


Load Calculator!

Length

m
km
in
ft
yards
miles
naut miles


Load Calculator!

Area

m2
km2
in2
ft2
miles2
acres


Load Calculator!

Volume

m3
liters
in3
ft3
us gal


Load Calculator!

Weight

kgf
N
lbf


Load Calculator!

Velocity

m/s
km/h
ft/min
ft/s
mph
knots


Load Calculator!

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O


Load Calculator!

Flow

m3/s
m3/h
US gpm
cfm


Load Calculator!

4 26

This website use cookies. By continuing to browse you are agreeing to our use of cookies! Learn more