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6 August, 04:05

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.

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  1. 6 August, 05:33
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    (h₁-h₂) = 2.30 10² m

    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
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