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Hydrostatic Forces Question_1

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known data

    At a particular point in the Pacific Ocean, the density of sea water increases non-linearly with depth according to p = p_o + m*z^2
    where p_o is the density at the surface, z is the depth below the surface, and m is a constant. Develop an algebraic equation for the relationship between pressure and depth.
    p(represents density, not pressure), P represents pressure.

    NB: ^ represents to the power of.... (eg z^2 is z squared)

    2. Relevant equations

    p = p_o + m*z^z ....(1)

    3. The attempt at a solution
    P = p_o*gz;
    p_o = P/gz;

    then From (1):
    p = (P/gz) + m*z^2
    but p = m/v so
    m/v = (P/gz) + m*z^2
    mgz(1/v - z^2) = P

    but F = mg

    so

    Fz(1/v - z^2) = P

    I know this is wrong but i really need help!!!
     
  2. jcsd
  3. Oct 8, 2007 #2

    Astronuc

    User Avatar

    Staff: Mentor

    p(z) = p_o + m*z^2 ....(1)

    Try dP(z) = p(z)g dz


    Then [tex] P(h) = \int_0^h\,\rho(z)\,g\,dz[/tex]
     
  4. Oct 11, 2007 #3
    Thanks!!
     
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