Here is a schematic cross-section of a water jet cutter nozzle design:
As it is shown, the thin water jet grabs abrasive particles in the mixing chamber and the mix flows through the nozzle.
My question is: what makes the water flow through the nozzle despite the loss of kinetic energy due to the abrasive material and the friction inside the nozzle instead of filling up the mixing chamber and running up in the ambient pressured abrasive feeding tube?
It's called Bernoulli's principle. It works because the fluid has momentum, so doesn't cause equal outward pressure at all points.
This principle can be used to convert a high-speed low-volume flow into a high-volume low-speed flow. Since the output flow has more volume than the input flow, additional material is sucked in.
The diameter of section 4 is a little larger than that of section 2 for this process to work.
As has been mentioned in other answers it is Bernoulli's principle. Part of the pressure in the water feed line turns into momentum and eject the jet. This jet now has a high velocity and a large momentum.
When this jet in part 3 picks up the abrasive sand and accelerates it to mix and carry it, there is some loss of momentum of water in nuzzle.
They have calibrated the feed of the abrasive material such that its inertia and friction is kept well below what can cause clogging of the nuzzle or backing up.
