Hi Dimitri,
You need to model the air that the water will be within also - did you have a chance to read the guide that was posted?
Something like this. Then we can just make the water inlet here.

The model would be set up with everything suppressed apart from the volume - which we call 'water' but as we do not assign a Height Of Fluid Initial Condition to it, this will act as air initially.
At the back we have a flow rate where the water will enter (I guessed 10 l/min) and I also left a P=0 on the very top.
Use a refinement region or similar where the water will flow

Turn on Free Surface and set the Gravity direction. Turning on the free surface will ensure that water enters at the condition we applied at the rear.
Once you switch this on, the solution will switch to transient, this is fine. We may need to reduce the timestep size but try it as is for now.
This is it meshed, with the suppressed parts turned back on and shaded. I also right clicked to show the Free Surface - which is just about entering the pipe at the rear.

We will likely need more mesh but I will leave that to you.
Does that help?
Jon