How is the momentum conserved inside of a fluid?

In summary, the conversation discusses a fluid dynamics problem involving two submarines of different densities moving at the same speed in a closed system. The problem is that while one submarine, being denser than the fluid, exchanges momentum with the system as it moves, the other submarine, having equal density to the fluid, does not. The conversation also explores the concept of center of mass and the role of drag and thrust in the exchange of momentum within the fluid. There is a question about how momentum is carried inside a fluid when the surroundings are all the same density, and it is clarified that the net momentum in the system remains constant regardless of the submarine's density.
  • #1
HS-experiment
9
1
Hello Physics Forums,

I have a fluid dynamics problem which appears to challenge some momentum principles.

Suppose you have two submarines (like below), identical in shape, but not in mass. One of the submarines has density equal to the fluid, while the other is denser. They move at the same speed. The body of water + submarine is a closed system, and the two submarines only exist for contrast and do not interact with one another.

two bodies in fluid.png


Because one of the submarines is denser than the fluid, it's movement changes the center of mass of the system. For this reason it must exchange momentum with the fluid as it moves. The other submarine is equal density to the fluid, so its movement around the system causes no change in center of mass, and so it does not exchange net momentum with the fluid.

EDIT: the center of mass does not change in either case. But, an outside observer will see a (very slight) shift in the position of the system as the denser sub moves around inside it.

How come the denser submarine exchanges momentum with the system while the lighter one does not?

If you divide the systems along the dotted line that goes through the propeller, there is not a difference between the right hand side of the diagram (equal velocities, equal drag, equal fluid dynamics). So it seems that the difference has to be on the left side of system (behind the propeller). Granted, the heavier submarine will need to push a larger volume of water to accelerate to the same speed as the lighter sub. But it seems like this would only change the magnitude of the momentum transfer and not eliminate it completely.
 
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  • #2
What happens if you look at the second system with the denser submarine from the perspective of its center of mass frame? Then by definition its center of mass is stationary.

What exactly do you mean by "exchange momentum" and why do you say that the denser submarine exchanges momentum with the fluid? Does it still do so if you look at it from its center of mass frame?
 
  • #3
HS-experiment said:
The body of water + submarine is a closed system
HS-experiment said:
it's movement changes the center of mass of the system
If water + submarine is an isolated system, then the velocity of its center of mass will not change, no matter which submarine you take.
 
  • #4
A.T. said:
If water + submarine is an isolated system, the velocity of its center of mass will not change, no matter which submarine you take.

Yes, that is clear now. Its been a while since I last looked at this case and I forgot the core of it. :blushing:

I guess what I am getting at is - how is momentum carried inside of a fluid, when its surroundings are all the same density? A plume of water traveling in the -x direction has a momentum, but it must displace an equal volume of water in the +x direction. So the net momentum of the plume+system is ... 0?
 
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  • #5
There's a certain amount of drag force which depends on the shape and speed of the submarine. The drag removes momentum from the submarine and puts it into the water. The propellers counter the drag... they put a backward momentum on the water and add a forward momentum to the submarine. If the submarine is moving at constant velocity, the drag and thrust cancel out. In either case, the final momentum is whatever you started with. The system with the heavier submarine started with more momentum, so it ends with more momentum.
 

1. What is the principle of momentum conservation in fluids?

The principle of momentum conservation in fluids states that the total momentum of a closed system remains constant unless an external force acts on it. This means that the total momentum before and after a fluid flows through a system will be the same.

2. How is momentum conserved inside of a fluid?

Momentum is conserved inside of a fluid due to the fact that fluids are made up of molecules that are constantly in motion. As the fluid flows through a system, the momentum of individual molecules may change, but the total momentum of the fluid remains constant due to the interactions between molecules.

3. Does the shape or size of a container affect the conservation of momentum in fluids?

No, the shape or size of a container does not affect the conservation of momentum in fluids. As long as the system is closed and there are no external forces acting on the fluid, the total momentum of the fluid will remain constant regardless of the container's shape or size.

4. How does the conservation of momentum in fluids relate to Bernoulli's principle?

Bernoulli's principle states that as the velocity of a fluid increases, the pressure decreases. This is due to the conservation of momentum, as the increase in velocity results in a decrease in pressure to maintain a constant momentum. This principle is often used in applications such as airplane wings and carburetors.

5. Can the conservation of momentum in fluids be violated?

In theory, the conservation of momentum in fluids cannot be violated. However, in real-world situations, there may be slight deviations due to factors such as friction or external forces. These deviations are typically very small and can be accounted for in calculations, but the principle of momentum conservation still holds true.

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