Question

Mercury is added to a cylindrical container to a depth d and then the rest of the cylinder is filled with water. If the cylinder is 0.4 m tall and the absolute (or total) pressure at the bottom is 1.2 atmospheres, determine the depth of the mercury. (Assume the density of mercury to be 1.36 104 kg/m3, and the ambient atmospheric pressure to be 1.013e5 Pa)

Answer 1

0.10839 m

Step-by-step explanation:

`P_1` = Atmospheric pressure = 1 atm = 101325 Pa

`P` = Total pressure at bottom of mecury = 1.2 atm

g = Acceleration due to gravity = 9.81 m/s²

h = d = Depth of mercury

`\rho_m` = Density of mercury =
`1.36* 10^4\ kg/m^3`

`\rho_w` = Density of water =
`1000\ kg/m^3`

Pressure at the bottom is of the cylinder is given by

`P_2=P_1+\rho_wgh\\\Rightarrow P_2=101325+1000* 9.81(0.7-d)`

Pressure at the bottom of mercury is

`P=P_2+\rho_mgh\\\Rightarrow 1.2* 101325=101325+1000* 9.81(0.7-d)+1.36* 10^4* 9.81* d\\\Rightarrow 1.2* 101325=123606d+108192\\\Rightarrow d=(1.2* 101325-108192)/(123606)\\\Rightarrow d=0.10839\ m`

The depth of the mercury is 0.10839 m