Question

The atmospheric pressure at the top and the bottom of a building is read by a barometer to be 98.5 kPa and 100 kPa, respectively. If the density of air is 1.2 kg/m^3, calculate the height of the building (in m).

Answer 1

127.42m

Step-by-step explanation:

The air pressure can be understood as the weight exerted by the air column on a body, for this case we must remember that the pressure is calculated by the formula P=αgh, Where P=pressure, h=gravity, h= height,α=density

So what we must do to solve this problem is to find the length of the air column above and below the building and then subtract them to find the height of the building, taking into account the above the following equation is inferred

h2-h1= building height=H

`H=(P1-P2)/(g\alpha )`

P1=100kPa=100.000Pa

P2=98.5kPa=98.500Pa

α=1.2 kg/m^3

g=9.81m/s^2

`H=(100000-98500)/((9.81)(1.2) )=127.42m`