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A How is the momentum conserved inside of a fluid?

  1. Feb 23, 2017 #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.
    Last edited: Feb 23, 2017
  2. jcsd
  3. Feb 23, 2017 #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?
  4. Feb 23, 2017 #3


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    If water + submarine is an isolated system, then the velocity of its center of mass will not change, no matter which submarine you take.
  5. Feb 23, 2017 #4
    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?
    Last edited: Feb 23, 2017
  6. Feb 23, 2017 #5


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    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.
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