Momentum of a Water Jet Impacting Plate

In summary, the momentum of the fluid is not conserved in this scenario due to external forces acting on it throughout the event. The total momentum of the fluid after the impact is 0 in the reference frame of the stationary plate. This is because the vertical downward force of the plate leads to a net change in momentum of the fluid, and the total radial velocity would add up to 0 since it's symmetric. Additionally, there is no horizontal force acting on the fluid, so the horizontal momentum must remain 0, and the vertical momentum must also be 0 since there is no vertical motion of the fluid after impact. Therefore, the reasoning that momentum is not conserved is correct, and this applies even in an ideal scenario without energy
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person123
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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).
 
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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.
 
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FAQ: Momentum of a Water Jet Impacting Plate

1. What is the definition of momentum in the context of a water jet impacting a plate?

Momentum is a physical quantity that describes the motion of an object. In the context of a water jet impacting a plate, momentum refers to the amount of force that the water exerts on the plate as it collides with it.

2. How is the momentum of a water jet impacting a plate calculated?

The momentum of a water jet impacting a plate can be calculated using the formula p = mv, where p is the momentum, m is the mass of the water jet, and v is its velocity.

3. What factors affect the momentum of a water jet impacting a plate?

The momentum of a water jet impacting a plate is affected by the mass and velocity of the water jet, as well as the angle and surface area of the plate that it is hitting.

4. How does the momentum of a water jet impacting a plate relate to the force exerted on the plate?

The momentum of a water jet impacting a plate is directly related to the force exerted on the plate. The greater the momentum of the water jet, the greater the force it will exert on the plate.

5. What are the real-world applications of studying the momentum of a water jet impacting a plate?

Studying the momentum of a water jet impacting a plate has practical applications in industries such as manufacturing, where water jets are used for cutting and shaping materials. It can also help in understanding the impact of water on structures such as dams and bridges.

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