Talk:Rankine–Hugoniot conditions

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Greater explanation needed

I find this article very difficult to understand. It seems to have much assumed knowledge, and many of the symbols are undefined. It would benefit greatly from practical examples and applications, and full definitions of symbols. (Not to mention reputable references) Sholto Maud 02:38, 31 May 2006 (UTC)

I have expanded this article with the intention of making it clearer and to provide some additional references. However, unfortunately, this subject does require some familiarity with thermodynamics and a reasonable level of mathematics. I hope this helps. Griffgruff (talk) 23:18, 6 July 2009 (UTC)

Problem on the energy flux equation

The last equation (energy flux) contains a unit mismatch, that is to say, different units are added.

The first component (e- Internal energy) is [Cv x T] (Cv- specific heat in constant volume, T- temperature) the unit is [J/mol]

The two other added parts are [P/roh] and [1/2 x u^2] both of which have the same unit [(m/sec)^2] yet different from the first (e).

I don't see how you can add the three [ e+P/roh+(1/2 x u^2) ].

... unless the equation is per unit mass...

Is it?

Yes. Lowercase e and ρ indicate that the quantities are specific (meaning, that they are per unit mass). Titoxd(?!? - cool stuff) 20:56, 1 March 2008 (UTC)

This is very complicated to understand, as it requires a great deal of knowledge, I will provide a simpler derivation of the Rankine-hugoniot equations using only simple algebra. —Preceding unsigned comment added by 86.160.174.17 (talk) 10:52, 31 August 2009 (UTC)

Inviscid

A shcok is always a dissipative phenomenon, requiring viscosity. The Rankine-Hugoniot relations only assume that the fluid is non-viscous outside the shock. — Preceding unsigned comment added by Mkovari (talkcontribs) 10:37, 16 November 2012 (UTC)

Error in 1D Euler equation - momentum equation

Correct me if I am mistaken, but I believe that equation number 2 i.e. 1-D euler momentum equation has a mistke in it : on the right hand side, shouldn't the convective term be :

${\displaystyle {\frac {\partial }{\partial x}}{\frac {\rho u^{2}}{2}}}$

${\displaystyle {\frac {\partial }{\partial x}}\rho u^{2}}$

--GLorieul (talk) 19:20, 4 March 2014 (UTC)

No, the momentum equation does not have a factor of 1/2 missing. To see why you can take a look at the derivation of these equations @ [1].Bbanerje (talk) 21:11, 5 March 2014 (UTC)

Derivation of Rankine-Hugoniot jump condition from PDE is wrong

Note that jump conditions (for discontinuous functions) could not be obtained from differential equations in principle, so the derivation oj jump conditions in section “The jump condition” is erroneous. Re-casting of differential equations in another form would result, for this approach, in another (incorrect) “conservation law”. For example, the equation
${\displaystyle {\frac {\partial u}{\partial t}}+u{\frac {\partial u}{\partial x}}=0}$

can be rewritten in two equivalent forms (for smooth solutions):

${\displaystyle {\frac {\partial u}{\partial t}}+{\frac {\partial u^{2}/2}{\partial x}}=0}$

and

${\displaystyle {\frac {\partial u^{2}/2}{\partial t}}+{\frac {\partial u^{3}/3}{\partial x}}=0}$,
so this way of reasoning would give two (contradictory) jump conditions.

Albina-belenkaya (talk) 20:36, 9 January 2015 (UTC)

For physical reasons behind jump conditions in nonlinear hyperbolic PDEs see PDE Notes by J. Shatah. Bbanerje (talk) 04:55, 12 January 2015 (UTC)
The Rankine -- Hugoniot conditions are not, of course, incorrect. What I mean is that the way of reasoning (i.e., derivation of jump conditions by integrating PDEs) is wrong. The right way is postulating the integral relations for hyperbolic system (or derivation of jump conditions from a more complicated system for viscous heat-conducting gas; in this case the shock wave is a narrow zone with large gradients). In present version of the article this point is not clearly stated. Albina-belenkaya (talk) 18:42, 12 January 2015 (UTC)
I agree that a more rigorous approach would be better. You could add a section below the textbook derivation to explain the problems with this approach and what the solution is. Bbanerje (talk) 00:20, 13 January 2015 (UTC)

Equations not in frame of shock

The article states that "In a coordinate system that is moving with the shock, the Rankine–Hugoniot conditions can be expressed as:" but the equations given are in the frame of the pre-shock medium, no? --129.11.68.6 (talk) 14:04, 8 October 2015 (UTC)