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Homework Help: Finding pressure with given radius

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data
    http://img585.imageshack.us/img585/613/labnotebookq.gif [Broken]

    Uploaded with ImageShack.us
    A Test tube filled with water i being spun around in an ultracentrifuge with constant angular velocity, w (w = omega). The test tube i slying along a radius and revolving in a horizontal plane. The free surface of the water is at radius r(0) (with smaller parenthesis) as shown

    a) show that the pressure at any raidus r within the tube is given by: P=1/2 (row)(omega)^2+P(atm)

    b)suppose that w=3.8x10^5 rad/s and r(0)=10cm, what is pressure at r=13
    Does it matter whether it's gauge or atmospheric pressure?

    question, is it asking whether gauge pressure and actually pressure are the same?

    2. Relevant equations
    centripetal accleration =v^2/r = r(omega)^2
    Pressure= P(atm) + (row)*g*h
    where row is density, g is gravity (or acceleration in this case), and h is dept
    density = (row) = m/V = mass over volume



    3. The attempt at a solution
    took simple approach
    a= r(omega)^2

    and used this "a" (acceleration) as"g" (gravity)
    and r-r(0) (since that's the dept of watr) as h
    so using Pressure= P(atm) + (row)*g*h
    P= P(atm) + (density of water)*r*(omega)^2*(r-r(0))
    in symbols :P
    P= P(atm)+p*r*w^2(r-r(0))
    but this doesn't match the answer ;)
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 5, 2011 #2
    This is how I would start, does this work?
     

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