Mach Number

An introduction to and a definition of the 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 velocity (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), lb_f/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 below 1, the flow velocity is lower than the speed of sound - and the speed is subsonic.
• If the mach number is ~ 1, the flow velocity is approximately like the speed of sound - and the speed is transonic.
• If the mach number is above 1, the flow velocity is higher than the speed of sound - and the speed is supersonic.
• If the mach number is far above 1, the flow velocity is much higher than the speed of sound - and the speed is hypersonic.

Example - Calculating an Aircrafts Mach Number

An aircraft flies at velocity 500 mph at an altitude of 35.000 ft. The surrounding temperature is -60 ^oF.

The sound velocity at this altitude with this temperature can be calculated as

c = [k R T]^1/2

    = [1,4 1716 (ft.lb/slug.^oR) (-60 + 460 (^oR))]^1/2

    = 980 ft/s

where

k = 1.4

R = 1716 (ft.lb/slug.^oR)

The velocity of the aircraft can be calculated as

v = 500 (mi/hr) 5280 (ft/mi) / 3600 (s/hr)

    = 733 ft/s

The Mach Number can be calculated as

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

= 0.75 - the aircraft is flying at subsonic speed

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

Web The Engineering ToolBox