User:Eguitar62/sandbox

For a flow to be considered incompressible, the divergence of the fluid must be zeros at all points in the flow.


 * $$ \nabla \cdot \mathbf{v} = 0 $$

By divergence theorem we can write the following



Substituting into this equation



Which implies that



Also going back to earlier:


 * $$ \nabla \cdot \mathbf{v} = {\partial u \over \partial x} + {\partial v \over \partial y} + {\partial w \over \partial z} = 0$$