The Q1D equations: Difference between revisions

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\underbrace{\frac{d}{dt}\iiint_{\Omega}\rho d{\mathscr{V}}}_{=0}+\oiint_{\partial \Omega}\rho {\mathbf{v}}\cdot {\mathbf{n}}dS=0
\underbrace{\frac{d}{dt}\iiint_{\Omega}\rho d{V}}_{=0}+\iint_{\partial \Omega}\rho {\mathbf{v}}\cdot {\mathbf{n}}dS=0
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\oiint_{\partial \Omega}\rho {\mathbf{v}}\cdot {\mathbf{n}}dS=-\rho_1 u_1 A_1+\rho_2 u_2 A_2
\iint_{\partial \Omega}\rho {\mathbf{v}}\cdot {\mathbf{n}}dS=-\rho_1 u_1 A_1+\rho_2 u_2 A_2
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