Is the Pressure $P_2$ caused by a reaction force to the fluid-fluid collision, or is it the result of the collisions of the water molecules with the walls at the neck of this experiment. The part which confuses me is that $P_2$ needs to be less than $P_1 $but $P_2$ is exerted over a longer distance and the pressure exerted by fluids is calculated by $hdg$. Is there a reason why $P_2$ is less than $P_1$?
Because the pipe on the right is smaller, but the same amount of mass flows per second through both sides, the flow on the right side is faster.
For the velocity of a bit of fluid to change as it moves, there must be a net force on it.
That net force come from the difference in pressure.