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<title>Gasdynamik</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Gasdynamik</span></h1>

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Dieser Artikel wurde in die Qualitätssicherung der Redaktion Physik eingetragen. Wenn du dich mit dem Thema auskennst, bist du herzlich eingeladen, dich an der Prüfung und möglichen Verbesserung des Artikels zu beteiligen. Der Meinungsaustausch darüber findet derzeit <b>nicht</b> auf der Artikeldiskussionsseite, sondern auf der <b>Qualitätssicherungs-Seite</b> der Physik statt. </div>

<p>Die <b>Gasdynamik</b> ist ein Fachgebiet der <a href="Str%C3%B6mungsmechanik" title="Strömungsmechanik">Fluidmechanik</a> bzw. <i>Strömungslehre</i> und setzt sich mit <a href="Kompressionsmodul#Kompressibilität" title="Kompressionsmodul">kompressiblen</a> (dichteveränderlichen) Strömungen auseinander. Es umfasst sowohl <i>externe Strömungen</i>, z. B. über <a href="Flugzeug" title="Flugzeug">Flugzeugen</a> oder <a href="Wiedereintritt" title="Wiedereintritt">Wiedereintritts</a>körpern (<a href="Space_Shuttle" title="Space Shuttle">Space Shuttle</a> oder Landekapseln von <a href="Raumschiff" title="Raumschiff">Raumschiffen</a>), als auch <i>interne Strömungen</i> durch <a href="D%C3%BCse" title="Düse">Düsen</a> und <a href="Diffusor_(Str%C3%B6mungsmechanik)" title="Diffusor (Strömungsmechanik)">Diffusoren</a>.

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<div class="mw-heading mw-heading2"><h2 id="Isentropen_Gasströmung"><span id="Isentropen_Gasstr.C3.B6mung"></span>Isentropen Gasströmung</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Gesetzmäßigkeiten_und_Annahmen"><span id="Gesetzm.C3.A4.C3.9Figkeiten_und_Annahmen"></span>Gesetzmäßigkeiten und Annahmen</h3></div>

<p>Wenn die Annahmen der <a href="Stromfadentheorie" title="Stromfadentheorie">Stromfadentheorie</a> erfüllt sind, kann eine Strömung als eindimensional beschrieben werden. Aufgrund der relativ geringen Dichte von Gasen kann in der Regel die Wirkung der <a href="Gravitation" title="Gravitation">Gravitation</a> vernachlässigt werden. Es wird für die mathematische Beschreibung des Weiteren angenommen, dass dem Gas keine Wärme zu- oder abgeführt wird und keine Reibungsverluste auftreten. Die <a href="Entropie_(Thermodynamik)" class="mw-redirect" title="Entropie (Thermodynamik)">Entropie</a> ist damit konstant. Und es gilt die <i>Isentropenbeziehung</i>:

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<annotation encoding="application/x-tex">{\displaystyle p\sim \rho ^{\kappa }}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1a5e282ef86ff7cc23eb4a1a7c89a96b247abb11.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.738ex; height:2.843ex;" alt="{\displaystyle p\sim \rho ^{\kappa }}" loading="lazy"></span></dd></dl>

<p>Der Energieerhaltungssatz kann wie folgt formuliert werden und sagt aus, dass die Summe aus kinetischer Energie und <a href="Enthalpie" title="Enthalpie">Enthalpie</a> längs des <a href="Stromfaden" title="Stromfaden">Stromfadens</a> konstant ist.

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<annotation encoding="application/x-tex">{\displaystyle {\frac {u^{2}}{2}}+c_{\text{p}}T=c_{\text{p}}T_{t}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/12b9bb89d305bfffa279ff1d5191535928a79b92.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.285ex; height:5.676ex;" alt="{\displaystyle {\frac {u^{2}}{2}}+c_{\text{p}}T=c_{\text{p}}T_{t}}" loading="lazy"></span> ist konstant</dd></dl>

<p>Es gilt die <a href="Kontinuit%C3%A4tsgleichung" title="Kontinuitätsgleichung">Kontinuitätsgleichung</a>, welche ausdrückt, dass keine Masse verloren geht. Der <a href="Massenstrom" title="Massenstrom">Massenstrom</a> längs des Stromfadens ist konstant.

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<annotation encoding="application/x-tex">{\displaystyle {\dot {m}}=\rho \cdot u\cdot A}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/da45f8fa1d96dd26c16350fdb6405d9a08442627.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.772ex; height:2.676ex;" alt="{\displaystyle {\dot {m}}=\rho \cdot u\cdot A}" loading="lazy"></span> ist konstant</dd></dl>

<p>Die Eigenschaften des Gases lassen sich durch die <a href="Thermische_Zustandsgleichung_idealer_Gase" title="Thermische Zustandsgleichung idealer Gase">Zustandsgleichung</a> des <a href="Ideales_Gas" title="Ideales Gas">idealen Gases</a> beschreiben.

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<annotation encoding="application/x-tex">{\displaystyle p=\rho \cdot R_{s}\cdot T\!\,}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/50fac53aaa1e16a2a33cccdd4acd4b43888e55c8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:13.321ex; height:2.676ex;" alt="{\displaystyle p=\rho \cdot R_{s}\cdot T\!\,}" loading="lazy"></span></dd></dl>

<p>Damit stehen vier Gleichungen zur Verfügung, um die vier Variablen (Geschwindigkeit <i>u</i>, Druck <i>p</i>, Temperatur <i>T</i>, Dichte <i>ρ</i>) eindeutig zu beschreiben. Mit einer mathematischen Umformung lassen sich die variablen Zustandsgrößen der Strömung als dimensionslose Beziehungen ausdrücken. Dabei wird Druck, Temperatur und Dichte auf die <a href="Ruhegr%C3%B6%C3%9Fe" title="Ruhegröße">Ruhegrößen</a> bezogen (Index t). Die Ruhegrößen beschreiben den Zustand, der sich einstellt, wenn die Strömung verlustfrei bis zum Stillstand verzögert würde. Bei einer Strömung, die aus einem großen Druckbehälter startet, sind Behälterdruck, -temperatur und -dichte die Ruhegrößen (Verlustfreiheit vorausgesetzt).

</p><p>Die Geschwindigkeit kann nicht auf den Ruhezustand bezogen werden (Division durch Null), aber als <a href="Machzahl" class="mw-redirect" title="Machzahl">Machzahl</a> <i>Ma</i> und <a href="Lavalzahl" class="mw-redirect" title="Lavalzahl">Lavalzahl</a> <i>M*</i> dargestellt werden. Dazu wird die <a href="Schallgeschwindigkeit" title="Schallgeschwindigkeit">Schallgeschwindigkeit</a> <i>c</i> herangezogen.

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<annotation encoding="application/x-tex">{\displaystyle c={\sqrt {\kappa R_{s}T}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c8a11554bb8c48064cffd1accff1977d10e6003f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.172ex; height:3.509ex;" alt="{\displaystyle c={\sqrt {\kappa R_{s}T}}}" loading="lazy"></span></dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle M\!a={\frac {u}{\sqrt {\kappa R_{s}T}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bc6b41f044f1466e7f51bae74c7edfb3daa1747e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:14.898ex; height:5.676ex;" alt="{\displaystyle M\!a={\frac {u}{\sqrt {\kappa R_{s}T}}}}" loading="lazy"></span></dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle M^{*}={\frac {u}{\sqrt {{\frac {2\kappa }{\kappa +1}}R_{s}T_{t}}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5cf61f70e4921c1958f6a5f2ea7099d19e20f2bc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:18.646ex; height:7.509ex;" alt="{\displaystyle M^{*}={\frac {u}{\sqrt {{\frac {2\kappa }{\kappa +1}}R_{s}T_{t}}}}}" loading="lazy"></span></dd></dl>

<div class="mw-heading mw-heading3"><h3 id="Dimensionslose_Beziehungen">Dimensionslose Beziehungen</h3></div>

<p>Die angegebenen dimensionslosen Größen sind <a href="Dimensionslose_Kennzahl" title="Dimensionslose Kennzahl">Ähnlichkeitskennzahlen</a> und können wie folgt ineinander umgerechnet werden.

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<td style="text-align:center"><b>Quadrat der <a href="Machzahl" class="mw-redirect" title="Machzahl">Machzahl</a></b>

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<td style="text-align:center"><b>Quadrat der <a href="Lavalzahl" class="mw-redirect" title="Lavalzahl">Lavalzahl</a></b>

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<td style="text-align:center"><b>Temperaturverhältnis</b>

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<td style="text-align:center"><b>Druckverhältnis</b>

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<td style="text-align:center"><b>Dichteverhältnis</b>

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<annotation encoding="application/x-tex">{\displaystyle M\!a^{2}\!\,}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/43b5df157b39cab6801417ed5a631728bdf2beeb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.339ex; height:2.676ex;" alt="{\displaystyle M\!a^{2}\!\,}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle M^{*2}\!\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {T}{T_{t}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4ad10eee068894498e3e5897952325c96ed921c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:3.02ex; height:5.509ex;" alt="{\displaystyle {\frac {T}{T_{t}}}}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {p}{p_{t}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5f8715cb59c1ea71c9671d86f51573e55000834.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.832ex; height:5.343ex;" alt="{\displaystyle {\frac {p}{p_{t}}}}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\rho }{\rho _{t}}}}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9ac3f4549de5a5169a72d38ede2966a29fc11abc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.864ex; height:5.343ex;" alt="{\displaystyle {\frac {\rho }{\rho _{t}}}}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle M\!a^{2}=\!\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle M\!a^{2}\!\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {M^{*2}}{1-{\frac {\kappa -1}{2}}(M^{*2}-1)}}}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {2}{\kappa -1}}\left({\frac {T_{t}}{T}}-1\right)}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {2}{\kappa -1}}\left[\left({\frac {p_{t}}{p}}\right)^{\frac {\kappa -1}{\kappa }}-1\right]}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ded4bb97f06e48b49834650768d15d435e407efc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:23.464ex; height:8.509ex;" alt="{\displaystyle {\frac {2}{\kappa -1}}\left[\left({\frac {p_{t}}{p}}\right)^{\frac {\kappa -1}{\kappa }}-1\right]}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {2}{\kappa -1}}\left[\left({\frac {\rho _{t}}{\rho }}\right)^{\kappa -1}-1\right]}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/34a16dc595dd900a36dfb5261f89e0b305ad883a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.843ex; height:7.509ex;" alt="{\displaystyle {\frac {2}{\kappa -1}}\left[\left({\frac {\rho _{t}}{\rho }}\right)^{\kappa -1}-1\right]}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle M^{*2}=\!\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {M\!a^{2}}{1+{\frac {\kappa -1}{\kappa +1}}(M\!a^{2}-1)}}}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle M^{*2}\!\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\kappa +1}{\kappa -1}}\left(1-{\frac {T}{T_{t}}}\right)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/50ea720eb3b42d9e5900b065e66ba85dd86344eb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.009ex; height:6.176ex;" alt="{\displaystyle {\frac {\kappa +1}{\kappa -1}}\left(1-{\frac {T}{T_{t}}}\right)}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {\kappa +1}{\kappa -1}}\left[1-\left({\frac {p}{p_{t}}}\right)^{\frac {\kappa -1}{\kappa }}\right]}</annotation>

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</mrow>

</mrow>

</msup>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {\kappa +1}{\kappa -1}}\left[1-\left({\frac {\rho }{\rho _{t}}}\right)^{\kappa -1}\right]}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf3bb00e58cfacbc9ec897473d5a00c0915182b3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:22.843ex; height:7.509ex;" alt="{\displaystyle {\frac {\kappa +1}{\kappa -1}}\left[1-\left({\frac {\rho }{\rho _{t}}}\right)^{\kappa -1}\right]}" loading="lazy"></span>

</td></tr>

<tr>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {T}{T_{t}}}=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/87643f42c0091635dd80824e07e91029e91e9ead.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:5.473ex; height:5.509ex;" alt="{\displaystyle {\frac {T}{T_{t}}}=}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</mrow>

</msup>

</mrow>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{-1}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2166236fa2eb93201aab420df8ce088905947b57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.274ex; height:6.509ex;" alt="{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{-1}}" loading="lazy"></span>

</td>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1-{\frac {\kappa -1}{\kappa +1}}M^{*2}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7938d9db740ae27863e9118e845c45e3c8befe8c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.556ex; height:5.343ex;" alt="{\displaystyle 1-{\frac {\kappa -1}{\kappa +1}}M^{*2}}" loading="lazy"></span>

</td>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {T}{T_{t}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4ad10eee068894498e3e5897952325c96ed921c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:3.02ex; height:5.509ex;" alt="{\displaystyle {\frac {T}{T_{t}}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {p}{p_{t}}}\right)^{\frac {\kappa -1}{\kappa }}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/722efb0244a8e0aea9665d01e9ea133ba472ac9d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.795ex; height:7.343ex;" alt="{\displaystyle \left({\frac {p}{p_{t}}}\right)^{\frac {\kappa -1}{\kappa }}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {\rho }{\rho _{t}}}\right)^{\kappa -1}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2f44ac07a14c08c6b40c2e6ed18e7fbb9d728364.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.565ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\rho }{\rho _{t}}}\right)^{\kappa -1}}" loading="lazy"></span>

</td></tr>

<tr>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {p}{p_{t}}}=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5a4b52dc7e45714031a42313e4a92184b40e9994.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:5.285ex; height:5.343ex;" alt="{\displaystyle {\frac {p}{p_{t}}}=}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</mrow>

</msup>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{\frac {-\kappa }{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/05736b8ec1814eebbdd6f263d1b9f526dba59e57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.484ex; height:7.176ex;" alt="{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{\frac {-\kappa }{\kappa -1}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</msup>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left(1-{\frac {\kappa -1}{\kappa +1}}M^{*2}\right)^{\frac {\kappa }{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f003d90952232b6cdb0d6a0299ba058e6a236daa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.519ex; height:7.009ex;" alt="{\displaystyle \left(1-{\frac {\kappa -1}{\kappa +1}}M^{*2}\right)^{\frac {\kappa }{\kappa -1}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {T}{T_{t}}}\right)^{\frac {\kappa }{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bae8a0bf0f0403b48c3f45b49ca3d13a2dd3a159.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.983ex; height:7.009ex;" alt="{\displaystyle \left({\frac {T}{T_{t}}}\right)^{\frac {\kappa }{\kappa -1}}}" loading="lazy"></span>

</td>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {p}{p_{t}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5f8715cb59c1ea71c9671d86f51573e55000834.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.832ex; height:5.343ex;" alt="{\displaystyle {\frac {p}{p_{t}}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {\rho }{\rho _{t}}}\right)^{\kappa }}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ff16ffc6936681cbccbd90d7b8ff17ffb5290c7e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:7.464ex; height:6.176ex;" alt="{\displaystyle \left({\frac {\rho }{\rho _{t}}}\right)^{\kappa }}" loading="lazy"></span>

</td></tr>

<tr>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {\rho }{\rho _{t}}}=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/16c14de3223d4dd8ae52c2267db7af967f7242ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:5.317ex; height:5.343ex;" alt="{\displaystyle {\frac {\rho }{\rho _{t}}}=}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</mrow>

</msup>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{\frac {-1}{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4f4ebc12e6a3c566a6b1972ce0f40b79a31b8192.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.484ex; height:7.343ex;" alt="{\displaystyle \left(1+{\frac {\kappa -1}{2}}{M\!a}^{2}\right)^{\frac {-1}{\kappa -1}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</msup>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left(1-{\frac {\kappa -1}{\kappa +1}}M^{*2}\right)^{\frac {1}{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/90a25026f9064d91bddf6187b7cce5097b02f1aa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.519ex; height:7.176ex;" alt="{\displaystyle \left(1-{\frac {\kappa -1}{\kappa +1}}M^{*2}\right)^{\frac {1}{\kappa -1}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {T}{T_{t}}}\right)^{\frac {1}{\kappa -1}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d891bf05334c43e44a1ae528d7616c287c20526e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:9.983ex; height:7.176ex;" alt="{\displaystyle \left({\frac {T}{T_{t}}}\right)^{\frac {1}{\kappa -1}}}" loading="lazy"></span>

</td>

<msup>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mfrac>

</mfrac>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left({\frac {p}{p_{t}}}\right)^{\frac {1}{\kappa }}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/34f844aee318090fd33c398927fd219b8663b854.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:8.09ex; height:7.176ex;" alt="{\displaystyle \left({\frac {p}{p_{t}}}\right)^{\frac {1}{\kappa }}}" loading="lazy"></span>

</td>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {\rho }{\rho _{t}}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9ac3f4549de5a5169a72d38ede2966a29fc11abc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.864ex; height:5.343ex;" alt="{\displaystyle {\frac {\rho }{\rho _{t}}}}" loading="lazy"></span>

</td></tr></tbody></table>

<div class="mw-heading mw-heading3"><h3 id="Verwendete_Formelzeichen">Verwendete Formelzeichen</h3></div>

<table>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a781f91991ad61e9a44d55637d68fa90961a9612.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T\!\,}" loading="lazy"></span></td>

<td>Temperatur (stets als absolute Temperatur in Kelvin)

</td></tr>

<tr>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T_{t}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/253f0bb55b3cbf03ee67d790726ff88857bac097.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.184ex; height:2.509ex;" alt="{\displaystyle T_{t}\!\,}" loading="lazy"></span></td>

<td><a href="Ruhetemperatur" class="mw-redirect" title="Ruhetemperatur">Ruhetemperatur</a>

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3312415e64b704854032e7c19fe1f4621d907a8d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p\!\,}" loading="lazy"></span></td>

<td>Druck (stets als absoluter Druck gegenüber Vakuum)

</td></tr>

<tr>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p_{t}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/424827231c12902333fb8a8c56413c1a778720c5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.085ex; height:2.009ex;" alt="{\displaystyle p_{t}\!\,}" loading="lazy"></span></td>

<td><a href="Ruhedruck" class="mw-redirect" title="Ruhedruck">Ruhedruck</a>

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rho \!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8dfe7f773266aa21dd37387252a399dbeebf0f7f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho \!\,}" loading="lazy"></span></td>

<td>Dichte

</td></tr>

<tr>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c_{\text{p}}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/800be62b50d74207a333098c6f4641dbb141e35f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.153ex; height:2.343ex;" alt="{\displaystyle c_{\text{p}}\!\,}" loading="lazy"></span></td>

<td><a href="Spezifische_W%C3%A4rmekapazit%C3%A4t" title="Spezifische Wärmekapazität">spezifische Wärmekapazität</a>

</td></tr>

<tr>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle R_{s}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/551ff540814ce42717b69a8264708b608bd79097.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.767ex; height:2.509ex;" alt="{\displaystyle R_{s}\!\,}" loading="lazy"></span></td>

<td><a href="Universelle_Gaskonstante#Spezifische_Gaskonstante" class="mw-redirect" title="Universelle Gaskonstante">spezifische Gaskonstante</a>

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \kappa \!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ec56180596f88f97104539b2291211bcfd7f634f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:1.676ex;" alt="{\displaystyle \kappa \!\,}" loading="lazy"></span></td>

<td><a href="Isentropenexponent" title="Isentropenexponent">Isentropenexponent</a>

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle u\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6aad233a2ba52cbecc22f431bdbcce2db851d59e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u\!\,}" loading="lazy"></span></td>

<td>Strömungsgeschwindigkeit

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/829863009c9092f792db1e6e878d6badcc6eb71c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c\!\,}" loading="lazy"></span></td>

<td><a href="Schallgeschwindigkeit" title="Schallgeschwindigkeit">Schallgeschwindigkeit</a>

</td></tr>

<tr>

<mover>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\dot {m}}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5e5f4a07134853e5d582aaf7be856461e36f4d36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:2.176ex;" alt="{\displaystyle {\dot {m}}\!\,}" loading="lazy"></span></td>

<td>Massenstrom

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/745c982d5d971c897d6ea28a7ebdc2b8cddb621a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A\!\,}" loading="lazy"></span></td>

<td>durchströmte Querschnittsfläche

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle M\!a\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5f6b31b9f34d866d68d48b3a7f41f107c378897d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.672ex; height:2.176ex;" alt="{\displaystyle M\!a\,}" loading="lazy"></span></td>

<td>Machzahl

</td></tr>

<tr>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle M^{*}\!\,}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/91436de18c192269879d3f1cdf203bb05a2cf590.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.553ex; height:2.343ex;" alt="{\displaystyle M^{*}\!\,}" loading="lazy"></span></td>

<td>Lavalzahl

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>

<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noresize noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Commons"></span></span></div><b><span class=""><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Aerodynamics?uselang=de"><span lang="en">Commons</span>: Gasdynamik</a></span></b> – Sammlung von Bildern, Videos und Audiodateien</div>

<ul><li><a href="Lavald%C3%BCse" title="Lavaldüse">Lavaldüse</a></li>

<li><a href="Machscher_Kegel" title="Machscher Kegel">Machscher Kegel</a></li>

<li><a href="Schallgeschwindigkeit" title="Schallgeschwindigkeit">Schallgeschwindigkeit</a></li>

<li><a href="Schallmauer" class="mw-redirect" title="Schallmauer">Schallmauer</a></li>

<li><a href="%C3%9Cberschallgeschwindigkeit" title="Überschallgeschwindigkeit">Überschallgeschwindigkeit</a></li>

<li><a href="Verdichtungssto%C3%9F" title="Verdichtungsstoß">Verdichtungsstoß</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<div class="sieheauch" role="navigation" style="font-style:italic;"><span class="sieheauch-text">Siehe auch</span>: <a href="Kinetische_Gastheorie" title="Kinetische Gastheorie">Kinetische Gastheorie</a>, <a href="Str%C3%B6mungsmechanik" title="Strömungsmechanik">Strömungsmechanik</a> und <a href="Thermodynamik" title="Thermodynamik">Thermodynamik</a></div>

<div class="mw-heading mw-heading3"><h3 id="Fachbücher"><span id="Fachb.C3.BCcher"></span>Fachbücher</h3></div>

<ul><li><a href="Klaus_Oswatitsch" title="Klaus Oswatitsch">Klaus Oswatitsch</a>: <cite style="font-style:italic">Grundlagen der Gasdynamik</cite>. Springer Vienna, Vienna 1976, ISBN 978-3-7091-8416-5, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-3-7091-8415-8">10.1007/978-3-7091-8415-8</a></span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=Klaus+Oswatitsch&rft.btitle=Grundlagen+der+Gasdynamik&rft.date=1976&rft.doi=10.1007%2F978-3-7091-8415-8&rft.genre=book&rft.isbn=9783709184165&rft.place=Vienna&rft.pub=Springer+Vienna" style="display:none"> </span></li>

<li>Klaus Oswatitsch: <cite style="font-style:italic">Spezialgebiete der Gasdynamik</cite>. Springer Vienna, Vienna 1977, ISBN 978-3-7091-8441-7, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-3-7091-8440-0">10.1007/978-3-7091-8440-0</a></span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=Klaus+Oswatitsch&rft.btitle=Spezialgebiete+der+Gasdynamik&rft.date=1977&rft.doi=10.1007%2F978-3-7091-8440-0&rft.genre=book&rft.isbn=9783709184417&rft.place=Vienna&rft.pub=Springer+Vienna" style="display:none"> </span></li>

<li>Jürgen Zierep: <cite style="font-style:italic">Theoretische Gasdynamik</cite> (= <cite style="font-style:italic">Wissenschaft + Technik Taschenausgaben</cite>). 4. Auflage. Braun, Karlsruhe 1991, ISBN 978-3-7650-2042-1.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=J%C3%BCrgen+Zierep&rft.btitle=Theoretische+Gasdynamik&rft.date=1991&rft.edition=4.+Auflage&rft.genre=book&rft.isbn=9783765020421&rft.place=Karlsruhe&rft.pub=Braun&rft.series=Wissenschaft+%2B+Technik+Taschenausgaben" style="display:none"> </span></li>

<li>Abraham Achterberg: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Gas Dynamics</cite>. Atlantis Press, Paris 2016, ISBN 978-94-6239-194-9, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.2991/978-94-6239-195-6">10.2991/978-94-6239-195-6</a></span> (englisch).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=Abraham+Achterberg&rft.btitle=Gas+Dynamics&rft.date=2016&rft.doi=10.2991%2F978-94-6239-195-6&rft.genre=book&rft.isbn=9789462391949&rft.place=Paris&rft.pub=Atlantis+Press" style="display:none"> </span></li></ul>

<div class="mw-heading mw-heading3"><h3 id="Klassiker">Klassiker</h3></div>

<ul><li><a href="Richard_Courant" title="Richard Courant">R. Courant</a>, <a href="Kurt_Otto_Friedrichs" class="mw-redirect" title="Kurt Otto Friedrichs">K. O. Friedrichs</a>: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Supersonic Flow and Shock Waves</cite> (= <cite class="lang" lang="en" dir="auto" style="font-style:italic">Pure and Applied Mathematics A Series of Texts and Monographs</cite>. <span style="white-space:nowrap">Band<span style="display:inline-block;width:.2em"> </span>1</span>). Interscience Publishers, New York 1948 (englisch, <a rel="nofollow" class="external text" href="https://archive.org/details/supersonicflowsh0001rcou">archive.org</a>).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=R.+Courant%2C+K.+O.+Friedrichs&rft.btitle=Supersonic+Flow+and+Shock+Waves&rft.date=1948&rft.genre=book&rft.place=New+York&rft.pub=Interscience+Publishers&rft.series=Pure+and+Applied+Mathematics+A+Series+of+Texts+and+Monographs" style="display:none"> </span></li>

<li><a href="Hans_Wolfgang_Liepmann" class="mw-redirect" title="Hans Wolfgang Liepmann">H. W. Liepmann</a>, <a href="Anatol_Roshko" title="Anatol Roshko">A. Roshko</a>: <cite class="lang" lang="en" dir="auto" style="font-style:italic">Elements of Gasdynamics</cite>. John Wiley & Sons, New York 1957 (englisch, <a rel="nofollow" class="external text" href="https://archive.org/details/elementsofgasdyn00liep/page/n5/mode/2up">archive.org</a>).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=H.+W.+Liepmann%2C+A.+Roshko&rft.btitle=Elements+of+Gasdynamics&rft.date=1957&rft.genre=book&rft.place=New+York&rft.pub=John+Wiley+%26+Sons" style="display:none"> </span></li>

<li><a href="Werner_Albring" title="Werner Albring">Werner Albring</a>: <cite style="font-style:italic">Angewandte Strömungslehre</cite>. De Gruyter, 1978, ISBN 978-3-11-261226-2, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1515/9783112612262">10.1515/9783112612262</a></span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Gasdynamik&rft.au=Werner+Albring&rft.btitle=Angewandte+Str%C3%B6mungslehre&rft.date=1978&rft.doi=10.1515%2F9783112612262&rft.genre=book&rft.isbn=9783112612262&rft.pub=De+Gruyter" style="display:none"> </span></li></ul>

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Normdaten (Sachbegriff): <a href="Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4019339-1">4019339-1</a></span> | <a href="Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85053291">sh85053291</a></span> | <a href="Web_NDL_Authorities" title="Web NDL Authorities">NDL</a>: <span class="-print"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlsh/00566027">00566027</a></span> </div>

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