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

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?

• What do you mean by modeling a flow with decreasing velocity/magnitude? You mean you have a decay for velocity magnitude at the inlet? Do you have any outlet? As long as your velocity is divergence free for an incompressible flow, you are satisfying the mass conservation no matter what. The only situation that I see it might give you some crazy nonsense result is that when you are pumping fluid into the computational domain with whatever flux but you don't have any outlet. As a result, you indeed breaks the mass conservation law and the thing that you are trying to solve doesn't make sense. Aug 24 '20 at 17:21
• No problem for conservation, for steady-state incompressible flow wherever the flux tube becomes narrow the flow would accelerate, wherever it becomes wider the flow would decelerate. For example, if you use a water hose with a nozzle for watering - it works just fine and the laws of universe are not visibly affected. Aug 24 '20 at 19:40

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?