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Estimate the density of the water

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Estimate the density of the water 5.7 km deep in the sea. (bulk modulus for water is B=2.0 x 10^9 N/m^2) By what fraction does it differ from the density at the surface?

    2. Relevant equations
    P=(rho)gh=F/A=B(delta l/l)

    3. The attempt at a solution
    So I have several equations above. I wanted so solve for rho using the first equation but I don't know pressure. I tried the second equations but I don't know Force or area. I tried the last equation but I would need delta l and l so basically I'm stuck. Some advice would be much appreciated.
     
  2. jcsd
  3. Apr 24, 2009 #2

    LowlyPion

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    Homework Helper

    Well they do say estimate. So maybe try to work it out assuming that p doesn't change?

    (Yes it changes, but does it change enough to matter? See what results you get and then decide.)
     
  4. Apr 24, 2009 #3
    I don't understand. I'm suppose to be solving for p at a certain density. How can it not change?
     
  5. Apr 24, 2009 #4

    LowlyPion

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    Have you calculated it using a uniform p as to the effect it will have on a bulk modulus of 2 * 109?
     
  6. Apr 24, 2009 #5
    In 6 km, the change in pressure is significant.

    Here's something to get you started:

    Use the equation,

    B=dP/(d(rho)/rho)

    Manipulate and integrate,

    integral of (d(rho)/rho) = integral of (dP/B)

    That results in,

    ln(rho2/rho1)=exp((P2-P1)/B)

    Where you can say state 1 is the surface, and state 2 is the state at 5.7 km down.

    You can then use the rho*g*h equation.
     
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