# 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.

https://brainmass.com/engineering/mechanical-engineering/hydrostatic-relation-empirical-formulas-113023

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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If the density is depending on the pressure, the above formula is no longer valid.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.