A long glass tube is evacuated and sealed shut at both ends

A long glass tube is evacuated and sealed shut at both ends. It is held in a vertical position, and the bottom end is inserted in a dish of mercury at atmospheric pressure. When a hole is punched in the bottom, how high does the mercury rise in the tube? If the same tube is inserted in a dish of water, how high will the water rise? (The density of mercury is 13.5 g/cm^3. The density of water is 1 g/cc. Assume the tube is long enough so that the liquid doesn\'t hit the top.)

Solution

Pressure by the fluid of height h with density = gh , g = 9.8 m/s²

At the bottom of tube is the the fluid surface where pressure is equivalent to 1 atmospheric pressure = 101325 N/m²

h = 101325/g = 10339.29/

For mercury = 13.5 g/cm³ = 13500 kg/m³

h_mercury = 76.59 cm

For water = 1 g/cm³ = 1000 kg/m³

hwater =   1033.93 cm