Question

A 1cm layer of a mystery liquid is on top of a 3m deep pool of water. The pressure at the bottom of the pool is 130808.5 Pa. The density of water is 1000kg/m^3. Show me how you find the density of the mystery liquid. What is the density of the mystery liquid? You must show your work. This problem is your opportunity to show me the physics concepts you know, take advantage of it, and include units.

Answer 1

h1-0.01m h3- 3m Water h2-3m-0.01m

You have three pressure point that they are marked with colors, first you need find the pressure in point two.

Apply the defintion of pressure in a liquid of uniform density, we have the following

$P_{3}-P_{2}=\rho _{water}.g.(h_{3}-h_{1})\rightarrow P_{2}=P_{3}+\rho _{water}.g.(h_{3}-h_{1})$

$P_{2}=(130808.5Pa)+(1000kg/m^{3}).(9.8m/s^{2}).[3m-0.01m]$

$P_{2}=160110.5Pa$

Secondly do the same procedure as before, but in the point two and one

$P_{2}-P_{1}=\rho _{mystery-liquid}.g.(h_{2}-h_{0})\rightarrow \rho _{mystery-liquid}=\frac{P_{2}-P1}{g.h_{2}}$

$\rho _{mystery-liquid}=\frac{(160110.5Pa)-(130130Pa)}{(9.8m/s^{2})(0.01m)}$

$\rho _{mystery-liquid}=305923.4kg/m^{3}$

If you have any question please let me know in the comments