Would modeling a fluid flow that decreases in magnitude violate conservation of mass?

Question

If I make a quasi-steady assumption in a model such as keeping the fluid density constant and assuming the flow is incompressible, does modeling a flow with decreasing velocity / magnitude, say, as the flow moves from left to right, violate conservation of mass?  If so, why?

MPIchael · Answer

The condition you are looking for is $nabla cdot mathbf{b} = 0$, whenever that is provided by the vector field, your density is preserved. Do you have an explicit example in mind?

Would modeling a fluid flow that decreases in magnitude violate conservation of mass?

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