On the first floor of the building, the barometer reads 760 mm Hg. Art. and on the roof – 758 mm Hg. Art.

On the first floor of the building, the barometer reads 760 mm Hg. Art. and on the roof – 758 mm Hg. Art. determine the height of the building if the average air density is 1.23 kg / m3.

Given:
P1 = 760 mm Hg column – air pressure on the first floor of the building;
P2 = 758 mm Hg column – air pressure on the roof of the building;
ro = 1.23 kg / m3 (kilogram per cubic meter) – air density;
ro1 = 13500 kg / m3 is the density of mercury.
It is required to determine h (meter) – the height of the building.
Let’s find the pressure difference between the roof and the first floor:
dP = P1 – P2 = 760 – 758 = 2 mm Hg = 0.002 meters Hg.
Then:
ro1 * dP * g = ro * g * h;
ro1 * dP = ro * h;
h = ro1 * dP / ro = 13500 * 0.002 / 1.23 = 27 / 1.23 = 22 meters (the result has been rounded to the nearest whole).
Answer: the height of the building is 22 meters.