Question

The mean density of sea water is r, and bulk modulus is B.The change in density of sea water in going from the surface of water to the depth of h is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{r}=\frac{\mathrm{M}}{\mathrm{V}} \\ \mathrm{where},\mathrm{M}=\mathrm{mass} \\ \mathrm{V}=\mathrm{volume} \\ \mathrm{r}=\mathrm{mean}\mathrm{density} \\ ∆\mathrm{r}=-\frac{∆\mathrm{V}}{{\mathrm{V}}^2}.\mathrm{M} \\ \frac{∆\mathrm{r}}{\mathrm{r}}=-\frac{∆\mathrm{VM}}{{\mathrm{V}}^2}\times \frac{\mathrm{V}}{\mathrm{M}}=-\frac{∆\mathrm{V}}{\mathrm{V}} \\ \mathrm{B}=-\frac{∆\mathrm{P}}{\left({\displaystyle \raisebox{1ex}{$∆\mathrm{V}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{V}$}\right.}\right)} \\ \mathrm{where},\mathrm{P}=\mathrm{pressure} \\ \mathrm{B}=\mathrm{bulk}\mathrm{modulus} \\ \mathrm{B}=\frac{\mathrm{hrg}\times \mathrm{r}}{∆\mathrm{r}} \\ ∆\mathrm{r}=\frac{{\mathrm{hr}}^2\mathrm{g}}{\mathrm{B}} \\ \mathrm{where},\mathrm{h}=\mathrm{depth} \end{gathered}$$