# How to calculate hydrostatic equilibrium?

I'm trying to solve the following problem. The sea level in the past was 200 m higher than today. The seawater became in isostatic equilibrium with the ocean basin. what is the increase in the depth $x$ of the ocean basins? Water density is $\rho_w = 1000\ kg\ m^{-3}$, and mantle density is $3300\ kg\ m^{-3}$.

Using the compensation column, I reach:

$$x = (\rho_w * 200\ m)/ 3300 = 60.60\ m$$

but normally I expected to find 290 m.

Can someone explain to me what's wrong?

• This won't solve all your problems, but the density of seawater is higher than that of fresh water. It's partly due to salinity. On this site seawater density varies from 1020 to 1035 kg/m3. (Seawater density)[hypertextbook.com/facts/2002/EdwardLaValley.shtml]
– Fred
Commented Jul 14, 2015 at 0:24
• Thank you for your comment. The exercise is based on Archimedes's principle rho_waterheight water = rho_mantleheight mantle. I'm not sure the density of water has anything to do here. When I compare the two columns with the compensation depth I don't find the result expected. I'm missing something but don't know what. Commented Jul 14, 2015 at 0:40
• This isn't my field of expertise but if you look at the picture [here] (en.wikipedia.org/wiki/Isostasy#/media/…) I'm thinking your case is like the middle picture. In the eqn for correct depth there's a term delta-SL(rho_/(rho_m - rho_w)). This will give you 286.86, which is near the 290 m you expected. If I could explain it, I'd give you a detailed answer.
– Fred
Commented Jul 14, 2015 at 13:11
• @user1166251 rho_water is the density of water. Commented Jul 14, 2015 at 15:15
• @user1166251 to clarify: you are asking for x for the case where sea level is 200m higher AND in isostatic equilibrium? Commented Nov 2, 2017 at 12:35

Applied to a water column over the mantle, you have to replace $\rho_c$ with your $\rho_w$. The total increase in ocean depth is $x = b_1 + h_1$, where $h_1$ are the 200 m extra sea level and $b_1$ is the depth increase to isostasy. Using the equation given in the link: $$x = \frac{h_1 \rho_w}{\rho_m - \rho_w} + h_1,$$
giving $x =$ 287 m