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thermofluids.html
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thermofluids.html
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<html>
<head>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/lib/p5.js"></script>
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']]
}
};
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<script id="MathJax-script" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
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<body>
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<main>
$$\begin{array}{cc}
T_1=T_2\land T_2=T_3\implies T_1=T_3&\text{0th law}\\
\Delta e=0&\text{1st law}\\
\Delta s\ge 0&\text{2nd law}\\
S=k\log W&\text{3rd law}\\
de=Tds-pdv&\text{combined 1st/2nd law}\\
p=\rho RT&\text{ideal gas law}
\end{array}$$
$$\begin{array}{cc}
\text{1d flow}\\
\hline
\rho_1u_1=\rho_2u_2\\
p_1+\rho_1u_1^2=p_2+\rho_2u_2^2\\
h_1+u_1^2/2=h_2+u_2^2/2\\
\end{array}$$
$$\begin{array}{c}
\text{shock wave}\\
\hline
M_2^2=\frac{M_1^2(\gamma-1)+2}{2\gamma M_1^2-(\gamma-1)}\\
\frac{T_2}{T_1}=\frac{h_2}{h_1}=\left(\frac{a_2}{a_1}\right)^2=1+\frac{2(\gamma-1)(M_1^2-1)(\gamma M_1^2+1)}{(\gamma+1)^2M_1^2}\\
\frac{p_2}{p_1}=1+\frac{2\gamma}{\gamma+1}(M_1^2-1)\\
\frac{\rho_2}{\rho_1}=\frac{u_1}{u_2}=\frac{(\gamma+1)M_1^2}{2+(\gamma-1)M_1^2}\\
\frac{p_{02}}{p_{01}}=\left(\frac{(\gamma+1)M_1^2}{2+(\gamma-1)M_1^2}\right)^{\frac{\gamma}{\gamma-1}}\left(\frac{\gamma+1}{2\gamma M_1^2-(\gamma-1)}\right)^{\frac{1}{\gamma-1}}\\
\tan\delta=2\cot\beta\frac{M_1^2\sin^2\beta-1}{M_1^2(\gamma+\cos 2\beta)+2}\\
M_{1n}=M_1\sin\beta\\
M_{2n}=M_2\sin(\beta-\delta)\\
\end{array}$$
</main>
</body>
</html>