In the bernoulli experiment, the pressure on one side is greater than the other, thus the fluid flows faster through the thinner nozzle.In the image, is the pressure created shown correctly? Since liquids are incompressible, I thought that through the neck of the experiment, the volume wouldn't equal to the volume which is being moved over a distance with a constant velocity. So, in short, my question is : Is the pressure P2 shown on the figure the pressure which does negative work on the shaded area? Also, is this negative work done because the water encounters collisions and pressure from the walls of the neck part?

• You can understand this flow without considering the pressure or Bernoulli's equation at all. The fluid flows faster in the areas with smaller cross section, as @ Farcher has correctly noted at the very beginning of his answer. You don't need any more detail than that. Feb 14, 2019 at 0:07

If the fluid is incompressible then the fluid would speed up if going from left to right as the volume flux of the fluid cannot change.
$$A_1v_1=A_2v_2$$ where $$A$$ is the area and $$v$$ is the speed.

In this case the fluid is made to move faster so is increasing in kinetic energy.

It is the pressure difference which provides the net force on the fluid which does the work on the fluid to increase its kinetic energy.

The force to the left $$P_1A_1$$ does positive work on the fluid and the force on the right $$P_2A_2$$ does negative work on the fluid.

There is a fuller explanation in Chapter 28 Fluid Dynamics.

Q: In the image, is the pressure created shown correctly?
A: Yes, but P1=P2 if there is no flow (velocity).

Q: Is the pressure P2 shown on the figure the pressure which does negative work on the shaded area?
A: No, but as The A2 is smaller than the A1 so the net Force is also less.

Yet, this Force-thinking is also not enough, neither is the work.
If you want to create the complete picture you need to think the conservation of the energy. The energy must be same if losses are neglected;
Think;
pressure (+ elevation) = potential energy.
velocity = kinetic energy

and you have everything balanced, when you keep energy constant. This means that increased velocity (kinetic energy) must reduce potential energy (pressure).

A main thing to keep in mind is Euler's finding that it is a Pressure Gradient that accelerates fluid. It is Newton in fluids. When you see an accelerating flow, you must look for the pressure gradient causing it. Energy conservation does indeed occur, but causes nothing as so many people try to claim, it is a Pressure Gradient that causes acceleration.

Few seem to realize that for the flow to the right in your diagram. the narrowing area is a restriction that is the cause of the higher pressure on the left. The higher pressure provides a net force to the right, thus accelerating the fluid toward the right.

While the flow was going on, if you slowly widened the right section, the pressure in the left would fall.