Question

On the desk, students have a straight, graduated cylinder that contains water up to a height h = 10cm and a Berzelius glass that contains oil. They add a volume of oil to the cylinder, equal to that of water. What hydrostatic pressure is exerted on the bottom of the vessel? See the adjacent figure (g = 10N / kg). The density of the oil is 0,8 g/ cm3 and the density of the water is 1g/cm3.

Answer 1

Pressure (p) is given by

$\begin{gathered} p=h\rho g \\ h=\text{ height of liquid column ;} \\ \rho=\text{ density of liquid ;} \\ g=\text{ acceleration due to gravity;} \end{gathered}$

Here, pressure has two parts -- one due to water column and second due to oil column .

Therefore

$\begin{gathered} p=h_1\rho_1g\text{ +h}_2\rho_2g\text{ }\begin{cases}h\placeholder{⬚}_1={h_2} \\ g={10\text{ N/kg}}\end{cases} \\ \\ p=\text{ \lparen10 }\times0.8\times10)\text{ +\lparen10}\times1\times10)\begin{cases}\rho_1={0.8} \\ \rho_2={1}\end{cases} \\ p=180\text{ N/ m}^2 \end{gathered}$

Final answer is :-

$pressure\text{ = 180 N/m}^2\text{ = 180 Pascal}$