QUESTION $3$

$15$ Marks

Consider the significant depths that can be reached in the ocean, where the compressibility of seawater becomes an important factor.

a$.$ Assuming the bulk modulus of seawater remains constant, derive a relationship between pressure and depth that accounts for the variation in fluid density with depth.

b$.$ Using the relationship derived in part $($a$),$ determine the pressure at a depth of $6$ km $,$ given that the bulk modulus of seawater is $2\mathrm{.}310Pa$ and its density at the surface is $1030$ kg $m^{-3}$

c$.$ Compare this result with the pressure calculated assuming a constant density of $1030$ kg $m^{-3}$