Question

A tank $5m$ high is filled with water up to $3m$ then is filled to the top with oil of density $0.85\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.$. Calculate the total pressure at the bottom of the tank due to these liquids.

Answer 1

Step 1: Given

Height of the tank = $5m$

Height of water = $3m$

Height of oil = $2m$

Density of oil ${\rho }_1$= $0.85\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.=850\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right.$

Density of water ${\rho }_2$= $1\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.=1000\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right.$

Step 2: Formula used and calculation

The pressure at the bottom of the tank is

$$\begin{gathered} P=h_1{\rho }_{1}g+h_2{\rho }_{2}g \\ \Rightarrow P=2\times 850\times 9.8+3\times 1000\times 9.8 \\ \Rightarrow P=16660+29400 \\ \Rightarrow P=46060Pa \\ \Rightarrow P=46.06kPa \end{gathered}$$

Hence, the total pressure at the bottom of the liquid is $46.06kPa$.