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Angular Momentum of Moving Water?

  1. Sep 10, 2011 #1
    A spinning top has angular momentum that creates a force that keeps it from falling over, and it precesses. Mass in motion has momentum and/or angular momentum.

    That made me wonder:

    Does fluid in motion create angular momentum?
    If so, how would it materialize?

    Consider a fictional example:
    Let’s say a river has a cross-sectional area of 1000 square metres and is flowing at 1 metre per second. In 1 second, the amount of water flowing through the cross section at a particular point would be 1000 cubic metres. That corresponds to 1,000,000 kilograms.
    Basically, a mass is flowing past a point at the rate of 1,000,000 kilograms per second.
    Would this mass in motion create a force that can be measured? For example, on a bridge above the river, would the period of a pendulum indicate that gravity is decreased (or increased) as opposed to a time when the water is still, but still the same volume of water in the test volume?

    At this point, I am not concerned about quantitative information; I just want to know if a force materializes by a moving fluid or not.
  2. jcsd
  3. Sep 10, 2011 #2


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    Staff: Mentor

    I believe moving water or any other fluid does indeed have angular momentum.
  4. Sep 10, 2011 #3

    Contribution to angular momentum of the system around the Origin, from part of volume dV = dx dy dzat at coordinate vector r(x,y,z) is

    ρv X r dxdydz where ρ is mass density of fluid and v is flow velosity.

    By integration in space we get the value of angular momentum of all the fluid.

    If the value changes by time, torque is applied to fluid from bank ,bottom of the floor or so on and vice versa.

  5. Sep 11, 2011 #4


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    That is a back-to-front way of looking at the situation.

    Angular (or even linear) momentum does not "create" any force, at least in clasical mechanics.

    If a top is spinning and you want to move it so it the axis is spinning in a different direction, you have to apply a lot of force to cancel out the origianal angular momentum and create the new momentum in a different direction, compared with the small force it would take to move the top if it was not spinning. That is not the same as saying the the top "creates a force".

    You can think of "precession" is a side-effect of the process of changing the angular momentum, because the top is a rigid body so the different parts of it can't move independently of each other.

    A fluid can have linear and angular momentum, but the different parts of a fluid can move in arbitrary directions and at different speeds relative to each other, so a rotating fluid doesn't usually behave in the same way a a rotating rigid bodys when you apply a force to it.
  6. Sep 12, 2011 #5
    Last edited by a moderator: Apr 26, 2017
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