Saturday, 25 July 2015

fluid dynamics - Unsteady and incompressible flow


In scientific literature, we know that the condition for incompressible flow is that the particular derivative of the fluid density $\rho$ is zero: $$ \frac{D\rho}{Dt}=0$$


and for steady flows the condition is that the partial derivative with respect to time is zero $\left(\dfrac{\partial \rho}{\partial t}=0\right)$.


However, the definition of the particular derivative is: $$\frac{D \rho}{Dt} = \frac{\partial \rho}{\partial t} + \left(\vec{v} \cdot \vec\nabla\right) \rho $$


The question is: if a flow is incompressible does that mean that the flow is necessarily steady? Can there be an unsteady and incompressible flow?




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