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A weatherman carried an aneroid barometer from the ground floor to his office atop the Sears Tower in Chicago. On the level ground, the barometer reads 30.15in.Hg.A; topside read 28.607in.Hg.A. The average atmospheric air density was 0.075 lb/cu.ft. Estimate the height of the building.

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Answer:

442.36038 m or 1451.31362 ft

Explanation:

[tex]P_1[/tex] = Initial pressure = 30.15 inHg

[tex]P_2[/tex] = Final pressure = 28.607 inHg

[tex]\rho[/tex] = Density of air  = 0.075 lb/ft³

[tex]1\ lb/ft^3=16.0185\ kg/m^3[/tex]

[tex]1\ in=0.0254\ m[/tex]

[tex]1\ m=3.28084\ ft[/tex]

Density of mercury = 13560 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

Difference in pressure is given by

[tex]P_1-P_2=\rho gh\\\Rightarrow h=\frac{P_1-P_2}{\rho g}\\\Rightarrow h=\frac{(30.15-28.607)\times 13560\times 0.0254\times 9.81}{0.075\times 16.0185\times 9.81}\\\Rightarrow h=442.36038\ m\\\Rightarrow h=442.36038\times 3.28084\\\Rightarrow h=1451.31362\ ft[/tex]

The height of the building is 442.36038 m or 1451.31362 ft

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