Question

The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of a building are 675 and 695 mm Hg, respectively, determine the height of the building. Take the densities of air and mercury to be 1.18 kg/m³ and 13,600 kg/m³, respectively.

Answer 1

(h₁-h₂) = 2.30 10² m

Step-by-step explanation:

The pressure depends on the height with the formula

P = P_atm + rho g h

Let's apply this expression for the building

P₁ = P_atm + rho_air g h₁

P₂ = P_atm + rho_air g h₂

Subtract

P₁ - P₂ = roh_air g (h₁ –h₂)

The measured pressure is in mm Hg to take this unit to units of pressure must be multiplied by the density of mercury and the acceleration of gravity

P₁- P₂ = rho_Hg g (h₁-h₂) _Hg

rho_Hg g (h₁-h₂) _Hg = roh_air g (h₁ –h₂)

(h₁ –h₂) = rho_Hg / rho_air (h₁-h₂) _ Hg

Let's calculate

(h₁-h₂) = 13600 / 1.18 (695-675)

(h₁-h₂) = 2.30 10⁵ mm

Let's reduce to meter

(h₁-h₂) = 2.30 10⁵ mm (1 m / 10³ mm)

(h₁-h₂) = 2.30 10² m