Question

For the continuity equation given by $\overrightarrow{\nabla }.\overrightarrow{V}=0$ to be valid, where $\overrightarrow{V}$ is the velocity vector, which one of the following is a necessary condition?

• A. Steady flow
• B. irrotational flow
• C. Inviscid flow
• D. Incompressible flow

Answer 1

The correct option is D Incompressible flow

$\overrightarrow{\nabla }.\overrightarrow{V}=0$

$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$

$\rho (\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z})=0$

So, the above equation represents Incompressible flow.