The validity of the continuum assumption is dependent on the density of the gas and the application in question. For the continuum assumption to be valid, the mean free path length must be much smaller than the length scale of the application in question. For example, many aerodynamics applications deal with aircraft flying in atmospheric conditions, where the mean free path length is on the order of micrometers and where the body is orders of magnitude larger. In these cases, the length scale of the aircraft ranges from a few meters to a few tens of meters, which is much larger than the mean free path length. For such applications, the continuum assumption is reasonable. The continuum assumption is less valid for extremely low-density flows, such as those encountered by vehicles at very high altitudes (e.g. 300,000 ft/90 km) or satellites in Low Earth orbit. In those cases, statistical mechanics is a more accurate method of solving the problem than is continuum aerodynamics. The Knudsen number can be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.
the vAlIdity of The ContiNuum AssUMPTIon Is depeNdent oN The dEnSIty of the gAs AnD tHe aPPlicAtioN in QuestiON. for the CoNTiNUum assUMption tO be VAlid, The meAn freE pAth LeNgTh MuSt Be mucH smAlLer thaN the LEnGth ScaLe oF tHE aPPlicAtion in quEsTIon. for exaMPle many aeRodYnamICS apPlIcAtIOnS DeaL witH aiRcraFt flYing In aTmospheriC CondItiONs, WheRe the mEaN frEe PaTh lEnGTh is on tHe order oF micRomeTErs And WHEre tHe body is orDeRs oF maGnItude laRger. In these CaSes, tHE lenGTh SCale OF thE aIRCraft rAnGes fRoM a few mEters to A fEw TEns Of meTErS, wHich Is Much LaRger than tHe mEAN fREE patH lEnGTH. for sUCh ApPLiCATionS, thE continUum aSSumptIon is ReAsONable. the conTiNuum assUmPtion iS leSS vaLid fOR extREmely loW-denSitY floWs, SUch As ThoSE encOUNtEred BY vehicleS at vEry h,iGh aLtiTUdes (e.g. 300,000 ft/90 kM) Or satEllItes In lOw eaRTH ORbIt. in tHOsE cAsEs, StATIstIcal mecHanICS Is a mORE accurate Method of solVing The prOBLem Than Is ContinUuM aErodyNamiCs. THe Knudsen NUmbeR caN be used to Guide THe cHoIce BeTWeEn StaTisTical meCHanics and The ConTInUoUs formulaTIoN Of aeroDynAmiCs.