Shock wave formation.

[Brian Abraham]

Your Airbus or Boeing airliner never gets close to Mach 1

Just taking a little liberty with the language as in a miss is as good as a mile Pug. Mmo of .9 of a 747 falls 10% short and gets to be how long is a piece of string sort of argument.

[Pugilistic Animus]

some helpful thermodynamics

If you were to take an elevator to the top of a building; and your friend took the stair and you both jumped who has the greater PE? as you see it doesn't matter the path [such functions were the path determines the amount of something are called 'path functions'....but any function that only depends on the initial and final states--and can be completely characterized by the initiall and final state are called state functions---like the bottom and top of that imaginary building----state functions are always written as 'delta somthing'

delta[E[internal enery],H[enthalpy,S [entropy]---but heat and work are path functions as a result of the PE available in the molecules of air as they are heated with compression---can be specified anyway---in others words---- you can assume an isothermal compression or an adiabatic compression, both different types of work and/or heat, but since the final quantities are equal---the work done to cause compression of the atmosphere on the airfoil..can be written by either equation [the one for isothermal or adiabatic] ---so lets look at those relations between the state functions and path functions--I need to do some light algebra--for this---and when I write d= I do not mean differentials--- I mean delta--final minus initial---

E is the internal energy of a gas[atmosphere] if you add to that the work of expansion/compression [PV work]--you get the Enthalpy [H] of the gas

So dH= dE+PV work ---if I subtract the wasted energy that is used to create disorder--entropy dS-- [which increases with temp]--

I have my Free energy ----dG

So I finally am left with dG = [E+pv work ==dH]----dG = dH - TdS---


there's
--more but I'll leave this to digest--so I can really be understood--I'll get to the point--- but I want to make sure I'm being understandable===and I wouldn't go too far ahead of me unless you're an engineer or scientist--because it may be hard to guess where I'm going---but it takes along time for me to get Tired

any questions so far?

I'll get to how it causes buffeting and all the good stuff--which is all to do with this ---but it's not an easy path for a non-specialist and it's hard to write math on Pprune and explain nice, but I'm not trying to be confusing--that's not hard to do for a few of us here if that's the goal



PA

[Pugilistic Animus]

The First Law

This has been a hard one for me cuz---I'm skipping special maths---{energy is the capacity to move stuff against a force [i.e do work]

The change in internal energy-Ef-Ei---a State function

The change in internal energy---is independent of path, but is composed of path functions--and for simplicity [in aerothermodynamics one excludes such paths as electrical work ] ---and IE is independent of volume perfect gases----

dE = Q[heat] + W [work] [both path functions]---

Assuming only adiabatic [no heat lost or gained] expansion work W = - Pex dV [look at the units]----then dE=w=-Pexdv


--the heat capacity [Cp] at constant pressure is equal = dH= dQ+Vdp[p=constant] so dH=dQ

and dE=CvdT [q=0] so [Work] adiabatic=Wad, but because of path independence ---I can say that dE [due to Wad] = work done isothermally---or electrically--if you want [dE=STATE function]

so CvdT [Wad]=-Pdv [isothermal work]


that's enuf--for me too---but I'll continue this it's a not easy to explain this ---any questions so far?

PA