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Hydrostatic relation

An empirical formula relating pressure and density for seawater w/ temperature held constant is:
p/pa = (k+1)(q/qa)^7 - k
where p= pressure
pa = pressure at the surface
k = dimensionless constant
q = density
qa = density at the surface
Using the formula in the hydrostatic relation, determine the pressure as a function of depth.
The hydrostatic relation is: p+dgz=constant
I am uncertain as to the proper approach for beginning this problem. I know that if I wanted to take the derivative of the empirical formula there must be a z term. I tried to insert P/RT in for q (q=P/RT) and then substitute for T with the relation T=T0-kz. But I wasn't for sure where to go from there.

Solution Preview

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Problem:

An empirical formula relating pressure and density for sea water w/ temperature held constant is: p/pa = (k+1)(/ a)^7 - k where p= pressure, pa = pressure at the surface,
k = dimensionless constant,  = density, a = density at the surface
Using the formula in the hydrostatic relation, determine the pressure as a function of depth.

Solution:

First of all, we need to remark that the well known hydrostatic formula:
(1)
is valid only if the density is constant.
If the density is depending on the pressure, the above formula is no longer valid.
I will prove that below, starting ...

Solution Summary

The solution uses the hydrostatic relation to determine the pressure as a function of depth. Hydrostatic relation constants are determined.

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