Consider the continuity equation \(\frac{\partial\rho}{\partial t}+\nabla.(\rho \vec{V})=0\). For an incompressible flow, this equation becomes ___________(a) \(\nabla.(\rho \vec{V})=0\)(b) \(\frac{\partial(\rho\vec{V})}{\partial t}=0\)(c) \(div(\vec{V})=0\)(d) \(div(\rho\vec{V})=0\)The question was posed to me in quiz.Origin of the question is Continuity Equation in portion 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 an incompressible flow, this equation becomes ___________(a) \(\nabla.(\rho \vec{V})=0\)(b) \(\frac{\partial(\rho\vec{V})}{\partial t}=0\)(c) \(div(\vec{V})=0\)(d) \(div(\rho\vec{V})=0\)The question was posed to me in quiz.Origin of the question is Continuity Equation in portion Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» Correct answer is (c) \(div(\VEC{V})=0\) The best explanation: TAKING the continuity equation, \(\frac{\PARTIAL\rho}{\partial t}+\nabla.(\rho \vec{V})=0\) For incompressible flow, ρ is CONSTANT \(\frac{\partial\rho}{\partial t}+\nabla.(\rho \vec{V})=0\) The resulting equation is \(\nabla.(\rho \vec{V})=0\) \(\rho\nabla.(\vec{V})=0\) \(\nabla.(\vec{V})=0\) Thus, for incompressible flow, divergence of \(\vec{V}=0\).

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