Question

Mercury is poured into a tall glass. Ethyl alcohol (which does not mix with mercury) is then poured on top of the mercury until the height of the ethyl alcohol itself is 141 cm. The air pressure at the top of the ethyl alcohol is one atmosphere. What is the absolute pressure at a point that is 7.49 cm below the ethyl alcohol-mercury interface?

Answer 1

Pressure in a fluid = P + ρgh

Where P = the overlying pressure
ρ = the density of the fluid
g = acceleration due to gravity
h = the distance from the fluid's surface

The density of ethanol is 789 kg/m³ and the density of mercury is 13546 kg/m³.

At the top of the ethanol column, P = 1 atm = 101325 Pa

At the bottom of the ethanol column, P = (101325 atm) + (789 kg/m³)(9.81 m/s²)(1.41 m)

P = (101325 Pa) + (10913.526 Pa) = 112238.526 Pa = 1.10770 atm

***

7.49 cm (0.0749 m) below the alcohol-mercury interface the pressure is:

P = (112238.526 Pa) + (13546 kg/m³)(9.81 m/s²)(0.0749 m)

P = (112238.526Pa) + (9953.180 Pa) = 122191.706 Pa = 1.20593 atm