Momentum of a Water Jet Impacting Plate

[person123]

TL;DR Summary

When a jet impacts a plate, is the momentum of the fluid conserved?

Suppose you have a jet of fluid (say water) traveling vertically upward at a constant velocity. It impacts a stationary horizontal plate and so moves radially outward in all directions. Assume that there's no energy loss during the impact, so the speed of the fluid remains constant. Is momentum of the fluid conserved, and what is the total momentum of the fluid after impact?

I believe the momentum is not conserved, since the fluid changes directions. The vertical downward force of the plate leads to a net change in momentum of the fluid. This is even in an ideal scenario without energy loss. I also believe the total momentum of the fluid after the impact is 0 (in the reference frame of the stationary plate). The total radial velocity would add up to 0 since it's symmetric. Alternatively, since there's no horizontal force, the horizontal momentum must remain 0, and the vertical momentum must be 0 as well since there's no vertical motion of the fluid after impact. Is my reasoning correct?

(For context for why I'm asking, I'm TAing a lab where this question was asked, and every group answered momentum is conserved or it's not conserved just because of frictional loss, so I want to make sure my reasoning is correct).

 

[kuruman]

If the fluid alone is the system, its momentum is not conserved because external forces are acting on it throughout the event you describe:

1. As soon as the fluid emerges from the nozzle and until it hits the plate, the external force of gravity acts on it and, therefore, its momentum is not conserved.
2. During the fluid's collision with the plate, the external force of the plate acts on it and, therefore, its momentum is not conserved.

There is only one criterion for determining whether momentum is conserved: whether an external force acts on the system or not. It follows that when two balls collide, the momentum of either ball is not conserved, but the momentum of the two-ball system is.