查看“︁兰金-雨贡纽条件”︁的源代码

[[File:Rankine Hugoniot Shock-en.svg|thumb|right|激波前后状态的示意图]]
'''兰金－雨贡纽条件'''（{{lang-en|Rankine–Hugoniot conditions}}）是指[[激波]]两侧状态间所满足的关系式，其名称源于[[苏格兰]]工程师、物理学家[[威廉·约翰·麦夸恩·兰金]]<ref name="[Ran-70]">{{Cite journal |last=Rankine |first=W. J. M. |authorlink=威廉·约翰·麦夸恩·兰金 |year=1870 |title=On the thermodynamic theory of waves of finite longitudinal disturbances |journal=Philosophical Transactions of the Royal Society of London |volume=160 |pages=277–288 |url=http://gallica.bnf.fr/ark:/12148/bpt6k559658/f328.image.r=Philosophical+Transactions+of+the+Royal+Society+of+London+1870.langEN |doi=10.1098/rstl.1870.0015 |format= |access-date=2016-11-16 |archive-date=2013-12-12 |archive-url=https://web.archive.org/web/20131212220818/http://gallica.bnf.fr/ark:/12148/bpt6k559658/f328.image.r=Philosophical+Transactions+of+the+Royal+Society+of+London+1870.langEN |dead-url=no }}</ref>与[[法国]]工程师、物理学家{{le|皮埃尔·昂利·雨贡纽|Pierre Henri Hugoniot}}。<ref name="[Hug-87]">{{Cite journal |last=Hugoniot |first=H. |year=1887 |language=fr |title=Mémoire sur la propagation des mouvements dans les corps et spécialement dans les gaz parfaits (première partie) [Memoir on the propagation of movements in bodies, especially perfect gases (first part)] |url=https://books.google.com/books?id=wccAAAAAYAAJ&pg=PA3#v=onepage&q&f=false |journal=Journal de l'École Polytechnique |volume=57 |pages=3–97 |access-date=2016-11-16 |archive-date=2019-07-27 |archive-url=https://web.archive.org/web/20190727071835/https://books.google.com/books?id=wccAAAAAYAAJ&pg=PA3#v=onepage&q&f=false |dead-url=no }}</ref>

对于满足[[欧拉方程 (流体动力学)|欧拉方程]]的[[完全气体|量热完全气体]]所产生的定常[[激波]]，兰金－雨贡纽条件可表示为：

<math>
\begin{align}
& \frac{\rho_2}{\rho_1} = \frac{u_1}{u_2} = \frac{(\gamma-1)+(\gamma+1)p_2/p_1}{(\gamma+1)+(\gamma-1)p_2/p_1} \\
& \frac{T_2}{T_1} = \frac{a_2^2}{a_1^2} = \frac{p_2}{p_1}\cdot\frac{(\gamma+1)+(\gamma-1)p_2/p_1}{(\gamma-1)+(\gamma+1)p_2/p_1}
\end{align}
</math>

其中<math>\rho</math>为气体[[密度]]、<math>u</math>为流速、<math>p</math>为[[压强]]、<math>T</math>为[[温度]]、<math>a</math>为[[音速]]、<math>\gamma</math>为[[绝热指数]]，下标1与2则分别表示激波前、后的状态。

== 参考文献 ==
{{reflist}}

[[Category:流体力学中的方程]]
[[Category:连续介质力学]]