Mathy...that's more of a description of the flow more than what the Mach mter is using, as an aside,
Old Smokey has posted the
EXACT and CORRECT equation like a million times here...READ!! he revealed important information on the topic of Mach meter calibration
The derivation would be as follows:
Bernoulli's equation derived ultimately in terms of the thermodynamic equations is obtained from the equation written in terms sound velocity 'a'...the slope of the isoentrope passing through -rho^2*a^2 and that is equivalent to [dp/dv]s ...
so a =[1/rho^2* [dp/dv]s}^1/2, since Mach= TAS/a
since EAS is CAS corrected for compressibility(EAS),...in turn EAS corrected for altitude density ration 'sigma' is TAS... the (dp/dv) term is determined using the adiabatic gas laws for adiabatic compressibility to introduce a correction term so rewriting all of the terms for Mach number CAS (dp/dv)*
sigma/[1/rho^2* [dp/dv]s]^1/2) after tons of algebra that I'm not doing
...will give you the Mach meter equation... there are other circumscribing elementary equation from thermodynamics that need to be applied and the above equation are in turn derived from basic principles of mechanics and thermodynamics...from fundamental thermodynamics laws the actual equation I'd estimate at 10 pages of algebra and calculus, maybe much more, if you where to really attempt the derivation from basic principles, I don't know, ...
I assume the original poster has some finite background in differential equations to be asking that type of question...I'm not gonna duit...
I forgot to add the slope of where the velocity gradient 'dv' approaches zero, or the stagnation point, or in yet other words,...lim dv--->0 ...but can not equal zero...as then the whole set of functions would be undefined...
I
think... I got this right, please double check, and let me no if I made an error I'm not looking at any txt book right now, not available...
