Calculating Pressure-Depth Relationship in the Pacific Ocean

[chimmy48]

Homework Statement

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)

Homework Equations

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

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!

 

[Astronuc]

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

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


Then $$P(h) = \int_0^h\,\rho(z)\,g\,dz$$

 

[chimmy48]

Thanks!