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Fluid mechanics: linear momentum Quick question

  1. Feb 20, 2013 #1
    Im confused with the sign convention... From my notes I have that for

    mass flow rate: Entering is -m and leaving is +m
    momentum : Entering (-m)(+v) and leaving is (+m)(-v)

    Example: for a rectangular control volume, lets say, left side is point 1 and right side is poinit 2. assume we need to hold it in place and flow is from point 1to point 2. If I apply the equation of momentum i get:
    (-m)(+v) + (m)(-v) = -Fx (discarding other forces just to simplify)
    rearange
    -mv -mv= -Fx. (a)

    What im doing wrong that the book says, that it is : -mv + mv = -Fx. (b)

    Im really confused because some exanples are done like (a) and others just freaking dont know like (b)
     
  2. jcsd
  3. Feb 23, 2013 #2

    BruceW

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    Homework Helper

    yes, it can be annoying when a book adopts a certain convention, but doesn't explicitly state what it is, and then even changes convention.

    In this specific question, it looks like you have written something equivalent to:
    momentum entering + momentum leaving = -Fx
    you do need to be careful with equations like this. For example, 'momentum entering' could possibly mean one of two things:
    1)The velocity at point one times by mass.
    2)The momentum change due to mass which has velocity inward to the rectangle (whether it comes in through point one or two).
    Also, 'momentum leaving' could be interpreted in several different ways:
    1)The change of momentum contained within the rectangle due to outward velocity at the surface (a negative number).
    2)The absolute value of the definition just above (which will then be a positive number).
    3)The velocity at point two times by mass.

    So, you need to be careful to distinguish between the different possible meanings. And I know how you feel, I remember getting frustrated about problems involving the momentum going into a rectangle, and what meaning was being used.
     
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