Subsonic flow:
as stated above The karman-Tsien relation is the most common [perhaps only??] relation used for calibrating the mach meter camwork in order to correct for compressibilty that the basic transport propertiesthat the root means square velocity of molecules in a gas c =3RT/M for a perfect gas from this on can show [eventually--from Newtonian flows] that the speed of sound can be written thermodynamically as c
s =gamma*[RT/M{molar mass}]^.5 further expansion shows that [gamma*pressure/d =c
s]
*gamma is the ratio of heat capacity of a gas at constant p/heat capacity at constant v [1.4] 'air'
for an ideal gas for a body traveling at low to high subsonic speeds where the shape of the waveform travels like the speed of sound the airflow--traveling down a pipe placed in such a flow is compressed; this compression is then followed by rarefaction but the mass flow at a particular velocity remain the same from the fluid dynamic principle of continuity,... this is the compressibilty error,...when there are no molecular interactions ...the perfect gas equation is valid and those conditions were assumed by those two mentioned guys and the relation obviously worked,...
now
supersonic flows
[I'll try to be 100% correct here]
when a body is traveling through a gas faster then the free airsteam several complications occur 1. ideal gas law do not apply, 2. the realtion of the free stream flows not continous 3. gamma is no longer a constant 4. the primary cause of all of these complication are intermolecular forces to further complicate matters air ahead of the pipe is at a different temperature than the air at the pipe,..the waves no longer move in an ordered manner they look like this <<...<<<,<<........>>>>,...etc.
there is a discontinuity of form,...
however the funny wave form impinging on a body as well as those traveling throgh the pipe have an 'unpredictable' complex form....that concept was what I meant to convey [not DAS
],...but the mass flow through the pipe is constant [again from continuity] so in order to describe both the affects of compressibilty and molecular forces the state variable defining them have to be corrected,...I'll try to keep this simple,...in general these intermolecular interactions are highly dependent on T,...the corrections for gamma and the coorection for the defining state variables [rather than attempting to define the wave in the tube] it is better to redifine the state variables [and gamma] in termes of the molecular interactions,...generally the best correction involve writing the ideal equation and the gamma value in terms of a Taylor expansion,...from that expansion the effects of the waveform ican then be corrected for at sonic and supersonic flows,..lastly I'm not going to try and derive the final form from my head
,...but using 'Poiseulle's formula' for a fluid moving throgh a tube of radius 'r' that dV/dt =[p1^2-P2^2]*pi^4/16l(nu)p0 where p1 and p2 are the pressures at the ends of the tube.....
by combining...that with corrected state variables as appropriate a similar but much more complex formula than the K_Ts is obtained for mach meter calibarion also completly independent of T as shown in the prior post and beacuse of the same reasoning it will cancel
OS---it IS true you don't flame
PA---I need to lie down
