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Fluid in rotating tube with different initial levels

  1. Jul 13, 2016 #1
    1. The problem statement, all variables and given/known data
    ddddddd.png

    2. Relevant equations
    Fluid in rotation

    3. The attempt at a solution
    This exercise is quite different from the classic one of fluidi in rotation. Before rotation starts the height in one branch is bigger than in the other, so I do not really know how to approach the problem.

    My main difficulty is: how can I determine the constant ##C## in the following expression in this case?

    $$p(r,z)=-\rho g z+\frac{1}{2} \rho \omega^2 r^2+C$$

    (The frame of reference considered has the ##z## axis towards up and placed on axis of rotation, ##r## is the radial coordinate)

    The fact is that I do not really know how to impose the condition for determinimg ##C## as a function of ##\omega## (which is what I want to determine). I think that, once ##C## is determined the rest of exercise is straightforward.

    So how can I determine ##C##?
     
  2. jcsd
  3. Jul 13, 2016 #2

    haruspex

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    In condition a), what is the height of the fluid in the open section? What is the pressure at its top?
     
  4. Jul 17, 2016 #3

    rude man

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    You can't use Bernoulli when the tube is rotated.
    Instead:
    What total centripetal force is needed to maintain the system in equilibrium when pA = 0.8e5 Pa?
    How is this force going to be provided?
     
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