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Homework Help: Object in equilibrium between 2 fluids

  1. Feb 4, 2016 #1
    1. The problem statement, all variables and given/known data
    if an object is in equilibrium at the interface of 2 fluids in an open tank, why do both provide upthrust?

    2. Relevant equations
    P=P' +dgh

    3. The attempt at a solution
    The upper fluid is not in contact with the lower part of the object, so why would the fluid provide an upward buoyant force? There is no area at which the fluid could exert a force.
    Yet almost all the questions I have seen that deal with such a principle equate mg with the buoyant force due to the lower and upper liquids.
  2. jcsd
  3. Feb 4, 2016 #2
    Find the pressure at the lower end of the block and you will understand where you are going wrong.
  4. Feb 4, 2016 #3
    That would be P0 + h1d1g + h2d2g + (h1+h2)(dobjectg), right?

    h1, h2 = heights of object in each liquid
    d1, d2 = their densities
    but how would this simplification help further?
  5. Feb 4, 2016 #4
    The pressure on the top of the block is P0.

    The pressure on the bottom of the block is P0 + h1d1g + h2d2g

    The difference in pressure between the bottom of the block and the top of the block is h1d1g + h2d2g.
    So the force is A(h1d1g + h2d2g)=V1d1g+V2d2g. But this is just equal to the sum of the weights of the displaced fluids.
  6. Feb 4, 2016 #5
    So we don't include the weight of the block when we write the pressure?
  7. Feb 4, 2016 #6
    No you don't.
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