Consider the continuity equation \(\frac{\partial\rho}{\partial t}+\nabla.(\rho \vec{V})=0\). For a steady flow this equation becomes ___________(a) \(\nabla.(\rho \vec{V})=0\)(b) \(\nabla.(\vec{V})=0\)(c) \(div(\vec{V})=0\)(d) \(curl(\vec{V})=0\)I had been asked this question during an internship interview.Question is from Continuity Equation in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Consider the continuity equation \(\frac{\partial\rho}{\partial t}+\na

1.	Consider the continuity equation \(\frac{\partial\rho}{\partial t}+\nabla.(\rho \vec{V})=0\). For a steady flow this equation becomes ___________(a) \(\nabla.(\rho \vec{V})=0\)(b) \(\nabla.(\vec{V})=0\)(c) \(div(\vec{V})=0\)(d) \(curl(\vec{V})=0\)I had been asked this question during an internship interview.Question is from Continuity Equation in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» The correct choice is (a) \(\nabla.(\rho \VEC{V})=0\) To explain I WOULD say: Taking the continuity equation, \(\frac{\PARTIAL\rho}{\partial t}+\nabla.(\rho \vec{V})=0\) For steady flow, flow variables do not vary with time. \(\frac{\partial\rho}{\partial t}=0\) Thus, for steady flow \(\nabla.(\rho \vec{V})=0\).

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