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Homework Help: Fluid mechanics - Conservation of mass problem

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Here is the question along with my attempt:

    As you see in my second equation there are two unknowns, A_out and dm/dt.

    I think my problem is that I don't exactly understand the equation. dm/dt is the net mass flow rate. For example if dm/dt is a positive number then there is more flowing into the nozzle than there is flowing out. In other words there is a build up of mass in the nozzle? I guess this isn't possible since we have a nozzle and that is why in this case dm/dt = 0? Because that is the only other way I can think of doing this problem but I am not too sure.

    In what case could dm/dt be positive? I am guessing when there is a tank that can be filled... But how do I know that the nozzle doesn't have a small pouch where the mass can build on itself...?

    Also when they say "mass flow rate through the nozzle" is this dm/dt or is it the mass flow INTO the inlet nozzle?


    Edit: for those who read through my solution attempt, there is a mistake in the last line where I did my conversion from 80cm^2 to 80m^2. the 100cm/1m needs to be flipped.
  2. jcsd
  3. Feb 10, 2013 #2

    Simon Bridge

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    dm/dt is usually the mass flow rate through the nozzle.
  4. Feb 10, 2013 #3
    The equation of continuity states that the flow rate past one cross section of a pipe needs to be the same as that through another cross section

    J = A1v1 = A2v2

    This gives you the volume flow rate. If multiplied by the density of the liquid one would get the mass flow rate passing through a cross section of the pipe.
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