Question

Compute the height in feet of a high building if the pressure at the ground floor is 30 in Hg and at the top of the building is 28.5 in Hg. Assume that the density of air is 0.075 lbm/ft^3.

Answer 1

Given: Pressure at the ground floor is 30 in Hg and at the top of the building is 28.5 in Hg. The density of air is 0.075 lbm/ft³.

To find:  The height in feet of the high building.

Solution:

• According to the formula,

        $\delta P = \frac{\rho gh}{k}$

   ⇒  $h = \frac{\delta P k}{\rho g}$

• Here, k is a constant whose value is 32.174 lbm-ft, δP is the change in pressure between the ground and the top, g is the acceleration due to gravity whose value is 32.174 ft s⁻² and ρ is the density of air.

        $h= \frac{1.5 * 32.174}{0.075 * 32.174}$

• But the above calculation will not give us the height of the building in feet.

• Hence, we will use the calculations mentioned below.

        $h= \frac{106.1229947\frac{lbf}{ft^{2}} * 1 \frac{lbm}{lbf} }{0.075\frac{lbm}{ft^{3} } }$

           $= 1414.973262 ft$

Therefore, the height in feet of the high building is 1414.973262 ft.