Code:
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\usepackage{ngerman}
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\begin{document}
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\psframebox[shadow=true,framesep=10pt]{\begin{tabular}{ll} Gegeben: & \(p_1=2\) bar \\ & \(T_1 = 293\) K \\ & \(c_1 = 7,499\) m/s \\ & \(p_a=1,01325\) bar \end{tabular}} & & \psset{linecolor=black} \psframebox[shadow=true,framesep=10pt]{ \begin{tabular}{cc} Gegeben: & p\textsubscript{0} \\ & T\textsubscript{0} \\ & p\textsubscript{a} \end{tabular}} \\
\psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} \(T_0=T_1+\cfrac{c_1^2}{2\cdot c_p}\) \\ \\ \(=293K+\cfrac{(7,499m/s)^2}{2\cdot 1005J/(kg\cdot K)}=293,028K\) \\ \\ \(p_0=2bar\cdot \left(\cfrac{293,028K}{293K}\right)^{\frac{1,4}{1,4-1}}=2,00066bar\) \end{tabular}} \\ & \psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} Dichte in Rohrleitung: \\ \\ \(\varrho_0=\cfrac{p_0}{R\cdot T_0}\) \\ \\ \(=\cfrac{2,00066bar}{287,14J/(kg\cdot K)\cdot 293,028K}\) \\ \\ \(=2,3778kg/m^3\) \end{tabular}} \\
& \psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} Kritisches Druckverhältnis: \\ \\ \(\cfrac{p_*}{p_0}=\left(\cfrac{2}{\kappa+1}\right)^{\frac{\kappa}{\kappa-1}}\) \\ \\ \(= \left(\cfrac{2}{1,4+1}\right)^{\frac{1,4}{1,4-1}} = 0,528\) \end{tabular}} \\
& \psdiabox[shadow=true,framesep=10pt]{\(\cfrac{p_a}{p_0} \leq \cfrac{p_*}{p_0}\)} \\
\psset{linecolor=black} \psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} Im Austrittsquerschnitt A stellt sich der \\Druck p\textsubscript{a} ein: \\ \\ \(p=p_a\) \\ \\ \(T=T_0\cdot \left(\cfrac{p}{p_0}\right)^{\frac{\kappa-1}{\kappa}}\) \\ \\ \(\varrho=\cfrac{p}{R\cdot T}\) \\ \\ \(c=\sqrt{\mathstrut 2\cdot c_p\cdot \left(T_0-T\right)}\) \end{tabular}} && \psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} Im Austrittsquerschnitt A stellt \\ sich der kritische Zustand ein: \\ \\ \(p=p_*=p_0\cdot \left(\cfrac{2}{\kappa+1}\right)^{\frac{\kappa}{\kappa-1}}\) \\ \\ \(=2,00066bar\cdot \left(\cfrac{2}{1,4+1}\right)^{\frac{1,4}{1,4-1}}=1,057bar\) \\ \\ \\ \(T=T_*=T_0\cdot \cfrac{2}{\kappa+1}\) \\ \\ \(=293,028\cdot \cfrac{2}{1,4+1}=244,190K\) \\ \\ \\ \(\varrho=\varrho_*=\cfrac{p_*}{R\cdot T_*}\) \\ \\ \(=\cfrac{1,057bar}{287,14J/(kg\cdot K)\cdot 244,190K}=1,5074kg/m^3\) \\ \\ \\ \(c=c_*=\sqrt{\mathstrut \kappa\cdot R\cdot T_*}\) \\ \\ \(=\sqrt{\mathstrut 1,4\cdot 287,14J/(kg\cdot K)\cdot 244,190K}=313,31m/s\) \end{tabular}} \\
& \psframebox[shadow=true,framesep=10pt]{\begin{tabular}{c} \(\dot{m}=\mu\cdot A\cdot \varrho\cdot c\) \\ \(=1\cdot 0,000314m^2\cdot 1,5074kg/m^3\cdot 313,13m/s\) \\ \(=0,1484kg/s\) \end{tabular}}
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}
\end{document}
Vielen Dank!
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