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Describe surfaces of equal pressure in a rotating fluid

  1. May 25, 2010 #1
    Hi, I am trying to solve a basic question from a Fluid dynamics text book. Could you help me with the answer? The question is as follows:

    A closed vessel full of water is rotating with constant angular velocity [tex]\Omega[/tex] about a horizontal axis. Show that the surfaces of equal pressure are circular cylinders whose common axis is at a height [tex]g/\Omega^{2}[/tex] above the axis of rotation.

    I don't know how to tackle this problem. Is there a technique in solving such theoretical questions?


    P.S:- This is not a homework or coursework question. I am also new to Physics forum, and hence, my question may not be appropriate for this section. In that case please tell me in which section I should pose fluid dynamics questions.
  2. jcsd
  3. May 25, 2010 #2

    Andy Resnick

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    Interesting question... I only have a partial answer, working from Tritton's 'Physical Fluid Dynamics'. In it, he starts with:

    [tex]\frac{Du}{Dt} =\frac{1}{\rho}\nabla p -\Omega \times \Omega \times r - 2\Omega \times u + \nu \nabla^{2} u +\rho g[/tex]

    So, assuming conservation of momentum, Du/Dt = 0. Also, the second term on the rhs can be written as
    [tex] -\nabla (\frac{1}{2}\Omega^{2}r^{2})[/tex]

    and combined to give a reduced pressure

    [tex]p - \frac{1}{2}\Omega^{2}r^{2}[/tex]

    Then, ignoring the Coriolus term and assuming inviscid flow, I can maybe see how you get the result you mention. Maybe...

    hope this helps.
  4. May 30, 2010 #3
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