Problem 2

We learned in class that fluids are usually incompressible, and gases are compressible. For very

large ocean-depths however, the assumption that fluids are incompressible breaks down. In this

question, we are analyzing the pressure and density at a depth of z = 10 km in the deep ocean.

Assume the density of seawater at the surface is p = 1030 kg/m³, and the bulk modulus of seawater

is K 2.3.10 Pa. Please consider the following two contrasting assumptions:

• Case 1: The density is constant across all depths

dP

dP

Case 2: The bulk modulus, K = P

dp

dV

30 Points

is constant across all depths

Part a: Calculate an expression for the pressure as a function of depth for both cases. Please note

all assumptions, and show all intermediate mathematical steps. Hint: for case 2, you will need to

rewrite the expression for the bulk modulus and substitute this in the hydrostatic pressure equation.

Part b: Plot the density and pressure as a function of depth for both cases in two figures (one for

density, one for pressure), up to a depth of z = 10 km.

Part c: How large (in percentage) is the error that you are making in your assumption for pressure

and density if you incorrectly assume that the ocean is incompressible? State this with respect to

your calculated values at the 10 km depth.