Question

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 1

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 \(\nabla.(\rho \vec{V})=0\).