1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Buoyancy Force on a Bubble

  1. Nov 19, 2008 #1
    First off, thanks in advance to anyone who can help at all. I've attempted to do a few things, and none of them seem to work...let me know what you think!

    THANK YOU!!!

    1. The problem statement, all variables and given/known data
    A sperical bubble of radius r has a volume v and a pressure p when just below the surface of a liquid of density d (top of bubble is tangent to the water level).

    Let F1 be the magnitude of the buoyant force on the bubble when it is at this location.. Assume P is the atmospheric pressure and that the temperatureof the liquid and bubble do not change with depth.

    Let the y-axis be vertical. Let the x-axis be the water level. The bubble (though it doesn't matter) is on the positive side of the x-axis).

    a) Show that the magnitude of the buoyant force (F2) on the bubble as a function of its vertical position y in the liquid is: F2 = F1 [ p / (p - d*g*y) ]

    b) If the liquid is water, show that the buoyant force is half the surface value at a depth of 10.3m.

    2. Relevant equations
    Buoyant Force = (density of liquid)(volume displaced)(gravity) = d*v*g

    3. The attempt at a solution

    a) We know that as the bubble descends in depth, it is moving in the negative-y direction. We also know that:

    Buoyant Force = d*v*g = d*(cross-sectional area)(depth)*g = d*A*(-y)*g

    What I don't understand, is why you would need to go any further, given the information that we have. However, the question has been asked so I must solve it, right : P

    If it helps at all, this question is in a chapter about the Ideal Gas Law (PV = nRT)

    My next best attempt was the following:

    we know that F2 = d*A*(-y)*g and that (by Ideal Gas Law) v = nRT/p
    F2 = d*A*(-y)*g = d*v*g
    F2 = d*A*(-y)*g = d*(nRT/p)*g (this gets P in the denominator)
    F2 = A*(-y) = nRT/p
    F2 = (nRT/p)/(A*(-y)
    F2 = (nRT)/[A*(-y)*(p)]
    F2 = (nRT)/[(pi*r^2)(-y)(p)]

    And thats as far as I get before I realize I'm really not getting anywhere!

    There must be an equation or formula or form that I am missing somewhere, because this is really not even close to the form we are asked to show...and I am positive if I had this "missing equation" I could finish this...


  2. jcsd
  3. Nov 20, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    How does pressure change with depth? How does the bubble's volume change with depth? Hint: Use the ideal gas law to get a simple ratio.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook