Answer to Question #257922 in Math for Joshua

Question

Find the pressure on the roof of Grand Hyatt Hotel Manila (one of the tallest building in the Philippines if its height is 1,043 ft.

Answer 1

Dependency of the barometric pressure on the altitude is given by the formula

$$P=P_0\exp(-\dfrac{Mg}{RT}h)$$

$$P_0=101.325\ kPa, g-=9.807\ m/s^2,$$

$$M=0.02896\ kg/mol, T=288.15\ K$$

$$R=8.3143\ (N\cdot m)/(mol\cdot K)$$

$h=1043\ ft=1043\cdot0.3048\ m=317.9064\ m$

$$P=101.325\ kPa\cdot$$

$$\exp(-\dfrac{0.02896\ kg/mol\cdot9.807\ m/s^2}{8.3143\ (N\cdot m)/(mol\cdot K)\cdot288.15\ K}\cdot317.9064\ m)$$

$$=97.775\ kPa$$

$$97.775\ kPa\approx28.8146\ inches\ Hg$$