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I am wondering why there is a flow in a diffuser: so according to Bernoulli when the flow speeds up, the dynamic pressure drops and the static pressure rises.

Assume there are no losses (in total pressure): So in a diffusor the static pressure in the wider area is higher than in the narrow area. So the fluid particles are fighting against the higher static pressure and use their kinetic energy to overcome this?

I once upon a time learned, that in order to have a flow, you need a pressure gradient, and the particles move from higher pressure to lower pressure area .. but here not?

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Yes, the fluid particles are fighting against the higher static pressure and use their kinetic energy to overcome this. It is like in a pendulum.

(In your first phrase everything is on contrary, unfortunately.)

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You say it all yourself, but somehow don't notice the meaning.

As you say, there is no loss in total pressure, so the dynamic pressure has to become the static pressure. Considering that, the static pressure can never get high enough to completely overcome the dynamic pressure to stop the flow. As long as a fluid under static pressure has anywhere to go, it will go there, meaning it will become dynamic pressure.

For a single molecule, there is no difference between dynamic and static pressure. It can only travel (gas) or push (liquid) in one direction at a time, which is the basis of the Bernoulli equivalent principal. This makes the concept of pressure in fluids interpretive. It does not describe or define what is going on in a fluid. It is a model making it possible to work with what goes on in a fluid.

Still, in order to have a flow, you need a pressure gradient, and the particles move from higher pressure to lower pressure area, which in this case is mainly to be found outside your diffuser.

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