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\Blatt{6}{WS 2003/2004, 1.12.2003}
         {Mechanik der Kontinua}
         {Prof. J.~L.~van~Hemmen}

\begin{deflist}{20.}

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\item[12.]
{\bf Ausströmungsgeschwindigkeit einer Flüssigkeit}
\par\smallskip
\begin{enumerate}
\item Berechnen Sie aus der Euler'schen Gleichung
\begin{displaymath}
  \partial_t \vek{v} + ( \vek{v} \circ \nabla ) \vek{v} = \vek{f} -
  \frac{1}{\varrho} \nabla p
\end{displaymath}
die stationäre Ausströmungsgeschwindigkeit einer Flüssigkeit aus einer
kleinen Öffnung im Boden eines bis zur Höhe $h$ gefüllten Gefäßes.
\item Man mache sich klar, dass die kinetische Energie der
  ausströmenden Flüssigkeit dem Verlust an potentieller Energie der
  Flüssigkeit im Gefäß entspricht.
\end{enumerate}


\item[13.]
{\bf Ausströmungsgeschwindigkeit eines Gases}
\par\smallskip
\begin{enumerate}
\item Berechnen Sie aus den Euler'schen Gleichungen die
  Ausströmungsgeschwindigkeit eines Gases, das aus einem Druckbehälter
  mit Innendruck $p_1$ in die Umgebung mit Druck $p_0$ strömt. Dabei
  gelte die Boyle-Mariott'sche Zustandsgleichung.
\item Man mache sich klar, dass die Energie dabei erhalten bleibt.
\item Unter Verwendung der Raketengleichung (Endgeschwindigkeit $v$,
  spezifischer Impuls $v_s$, Gesamtmasse der Rakete $m_{ges}$ , Masse
  ohne Treibstoff $m_L$)
  \begin{displaymath}
    v = v_s \ln\left(\frac{m_{ges}}{m_L}\right)
  \end{displaymath}
  und des Ergebnisses von Aufgabe 12 mache man sich Vor- und
  Nachteile gasgetriebener gegenüber wassergetriebenen Raketen klar.
\end{enumerate}





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\footnotesize
\rule[.5mm]{\textwidth}{0.1mm}\\
Besprechung der "Ubungen am 8.12.2003 um 14.15 Uhr im Raum PH 127
(Garching).\\
"Ubungsleitung: Moritz Franosch, mail@Franosch.org, http://www.physik.tu-muenchen.de/lehrstuehle/T35/.



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