Question #257782
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.
1
Expert's answer
2021-10-28T17:42:01-0400

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


P=P0exp(MgRTh)P=P_0\exp(-\dfrac{Mg}{RT}h)

P0=101.325 kPa,g=9.807 m/s2,P_0=101.325\ kPa, g-=9.807\ m/s^2,

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

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

a. h=1043 ft=10430.3048 m=317.9064 mh=1043\ ft=1043\cdot0.3048\ m=317.9064\ m



P=101.325 kPaP=101.325\ kPa\cdot

exp(0.02896 kg/mol9.807 m/s28.3143 (Nm)/(molK)288.15 K317.9064 m)\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

97.775 kPa28.8146 inches Hg97.775\ kPa\approx28.8146\ inches\ Hg


b. h=2922 mh=2922\ m



P=101.325 kPaP=101.325\ kPa\cdot

exp(0.02896 kg/mol9.807 m/s28.3143 (Nm)/(molK)288.15 K2922 m)\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

71.660 kPa21.1613 inches Hg71.660\ kPa\approx21.1613\ inches\ Hg





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