The three-dimensions continuity equation in Cartesian co-ordinate system for incompressible fluid is

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

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