A continuity equation for two dimensional compressible flow is given by:

1
\(\frac{{\partial u}}{{\partial x}}\; + \;\frac{{\partial v}}{{\partial x}}\left( {\rho uv} \right)\; = 0\)
2
\(u\frac{{\partial u}}{{\partial x}}\; + v\frac{{\partial v}}{{\partial x}}\; = 0 \)
3
\(\frac{{\partial \left( {\rho u} \right)}}{{\partial x}}\; + \;\frac{{\partial \left( {\rho v} \right)}}{{\partial y}} = 0 \)
4
\(\frac{{\partial u}}{{\partial x}}\; + \;\frac{{\partial v}}{{\partial x}}\; = 0 \)

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