# Determine the depth of the Mine if at the bottom of the Mine the barometer shows a pressure

**Determine the depth of the Mine if at the bottom of the Mine the barometer shows a pressure of 106.2 kPa on the Earth’s surface p0 = 101.3 kPa.**

P1 = 106.2 kPa = 106.2 * 10 ^ 3 Pa.

Po = 101.3 kPa = 101.3 * 10 ^ 3 Pa.

g = 9.8 m / s ^ 2.

ρ = 1.2 kg / m ^ 3.

H -?

The depth of the mine H is determined by the difference: H = h1 – hо, where ho is the height of the air column on the surface of the earth, h1 is the height of the air column on the surface of the bottom of the mine.

The hydrostatic air pressure is determined by the formula: P = ρ * g * h. Where ρ is the density of air, g is the acceleration of gravity, h is the height of the air.

The pressure above the earth’s surface will be determined by the formula: Po = ρ * g * hо.

ho = Po / ρ * g.

The pressure above the surface of the bottom of the mine will be determined by the formula: P1 = ρ * g * h1.

h1 = P1 / ρ * g.

Н = P1 / ρ * g – Po / ρ * g = (P1 – Po) / ρ * g.

H = (106.2 * 10 ^ 3 Pa – 101.3 * 10 ^ 3 Pa) / 1.2 kg / m ^ 3 * 9.8 m / s ^ 2 = 416 m.

Answer: the depth of the mine is H = 416 m.