Answer to Question #257782 in Math for Aldrie

Question

a. Find the pressure on the roof of Grand Hyatt Hotel Manila (one of the tallest buildings in the Philippines if its height is 1,043 feet. b. Find the pressure on the top of Mount Pulag which is 2,922 meters tall.

Answer 1

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

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

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

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

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

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

$$P=101.325\ kPa\cdot$$

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

$$=97.775\ kPa$$

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

b. $h=2922\ m$

$$P=101.325\ kPa\cdot$$

$$\exp(-\dfrac{0.02896\ kg/mol\cdot9.807\ m/s^2}{8.3143\ (N\cdot m)/(mol\cdot K)\cdot288.15\ K}\cdot2922\ m)$$

$$=71.660\ kPa$$

$$71.660\ kPa\approx21.1613\ inches\ Hg$$