On the first floor of the school building, the barometer shows a pressure of 755 mm Hg. Art., and on the roof

On the first floor of the school building, the barometer shows a pressure of 755 mm Hg. Art., and on the roof – 753 mm Hg. Art. Determine the height of the building.

h1 = 755 mm = 0.755 m.
h2 = 753 mm = 0.753 m.
g = 9.8 m / s ^ 2.
ρp = 13546 kg / m ^ 3.
ρw = 1.2 kg / m ^ 3.
H -?
The hydrostatic pressure shown by the barometer is determined by the formula: P = ρр * g * h.
Where ρ is the density of the liquid in the barometer, g is the acceleration of gravity, h is the height of the liquid in the barometer.
P1 = ρр * g * h1.
P2 = ρр * g * h2.
The air column has the same pressure: P = ρw * g * H, where ρw is the air density, H is the height of the air per person.
P1 = ρв * g * Н1.
P2 = ρw * g * H2.
ρр * g * h1 = ρв * g * Н1.
Н1 = ρр * g * h1 / ρв * g = ρр * h1 / ρв.
ρp * g * h2 = ρw * g * H2.
H2 = ρр * g * h2 / ρв * g = ρр * h2 / ρв.
Н = Н1 -Н2 = ρр * h1 / ρв – ρр * h2 / ρв = ρр * (h1 – h2) / ρв.
H = 13546 kg / m ^ 3 * (0.755 m – 0.753 m) / 1.2 kg / m ^ 3 = 22.6 m.
Answer: the height of the building is H = 22.6 m.