Knudsen Number - Relationship To Mach and Reynolds Numbers in Gases

Relationship To Mach and Reynolds Numbers in Gases

The Knudsen number can be related to the Mach number and the Reynolds number:

Noting the following:

Dynamic viscosity,

Average molecule speed (from Maxwell-Boltzmann distribution),

thus the mean free path,

dividing through by L (some characteristic length) the Knudsen number is obtained:

where

  • is the average molecular speed from the Maxwell–Boltzmann distribution,
  • T is the thermodynamic temperature,
  • μ is the dynamic viscosity,
  • m is the molecular mass,
  • kB is the Boltzmann constant,
  • ρ is the density, .

The dimensionless Mach number can be written:

where the speed of sound is given by

where

  • U is the freestream speed,
  • R is the Universal gas constant, (in SI, 8.314 47215 J K−1 mol−1),
  • M is the molar mass,
  • is the ratio of specific heats, and is dimensionless.

The dimensionless Reynolds number can be written:

Dividing the Mach number by the Reynolds number,

and by multiplying by ,

yields the Knudsen number.


The Mach, Reynolds and Knudsen numbers are therefore related by:

Read more about this topic:  Knudsen Number

Famous quotes containing the words relationship to, relationship, mach, reynolds, numbers and/or gases:

    Whatever may be our just grievances in the southern states, it is fitting that we acknowledge that, considering their poverty and past relationship to the Negro race, they have done remarkably well for the cause of education among us. That the whole South should commit itself to the principle that the colored people have a right to be educated is an immense acquisition to the cause of popular education.
    Fannie Barrier Williams (1855–1944)

    I began to expand my personal service in the church, and to search more diligently for a closer relationship with God among my different business, professional and political interests.
    Jimmy Carter (James Earl Carter, Jr.)

    Physics is experience, arranged in economical order.
    —Ernst Mach (1838–1916)

    My dear dear Mother,
    If you don’t let me come home I die—I am all over ink,
    and my fine clothes have been spoilt—I have been tost in a blanket, and seen a ghost.
    I remain, my dear dear Mother,
    Your dutiful and most unhappy son,
    Freddy.
    P.S. Remember me to my Father.
    —Frederick Reynolds (18th century)

    I’m not even thinking straight any more. Numbers buzz in my head like wasps.
    Kurt Neumann (1906–1958)

    The bird is not in its ounces and inches, but in its relations to Nature; and the skin or skeleton you show me, is no more a heron, than a heap of ashes or a bottle of gases into which his body has been reduced, is Dante or Washington.
    Ralph Waldo Emerson (1803–1882)