# Hydrostatic Forces Question_1

1. Oct 7, 2007

### chimmy48

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. Oct 8, 2007

### Staff: Mentor

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

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

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

3. Oct 11, 2007

Thanks!!