Hydrostatics Relation for Seawater Pressure with Temperature Variation

[srh]

Homework Statement

An empirical formula relating pressure and density for seawater w/ temperature constant is:
p/pa = (k+1)(d/da)^7-k
pa - pressure condition on the surface
da - density condition on the surface
k - dimensionless constant
Using this formula in the hydrostatics relation, determine the pressure as a function of depth.

Homework Equations

Hydrostatic relation: dp/dz = -dg where d is density
T=T0-kz
d=P/RT

The Attempt at a Solution

I tried to replace d w/ P/RT and then T w/ T0-kz to get the equation in terms of z. When I tried to take the derivative it was getting very complicated and I couldn't get it to work. I think I'm just approaching the problem incorrectly. I was wondering exactly how to start this problem. I know in order to take the derivative w/ respect to z there needs to be a z in the equation.

 

[teknodude]

Why do you need to differentiate with the hydrostatic relation?