Respuesta :
Answer:
Local atmospheric pressure in kPa = 97.932 kPa
Local atmospheric pressure in mm Hg = 734.78 mm Hg
Explanation:
Given:
- [tex]P_a[/tex] = absolute pressure = 46 kPa = 46000 kPa
- [tex]\rho_a[/tex] = density of air = [tex]0.828\ kg/m^3[/tex]
- [tex]\rho_h[/tex] = density of mercury = [tex]13600\ kg/m^3[/tex]
- [tex]h[/tex] = altitude of the plane = 6400 m
Assume:
- [tex]P_h[/tex] = pressure decrease due to air at height h
- [tex]P_{atm}[/tex] = local atmospheric pressure
As we go up the altitude, the pressure decreases. So, the reading of the pressure will be equal to the decrease in pressure due to height subtracted from the local atmospheric pressure.
[tex]\therefore Absolute\ pressure = Atmospheric\ pressure - Pressure\ decrease\\\Rightarrow P_a=P_{atm}-P_h\\\Rightarrow P_{atm}=P_a+P_h\\\Rightarrow P_{atm}=46000+\rho_a g h\\\Rightarrow P_{atm}=46000+0.828\times 9.8\times 6400\\\Rightarrow P_{atm}=97932.16\ Pa\\\Rightarrow P_{atm}=97.932\ kPa[/tex]
Now, conversion of the local atmospheric pressure is quite simple. let us assume that height of H mm of Hg is required to exert a pressure equivalent to the local atmospheric pressure.
[tex]\therefore P_{atm}= \rho_h g H\\\Rightarrow H = \dfrac{P_{atm}}{\rho_h g}\\\Rightarrow H = \dfrac{97932.16\ Pa}{13600\ kg/m^3 \times 9.8\ m/s^2}\\\Rightarrow H = 0.73478\ m\\\Rightarrow H =734.78\ mm[/tex]
Hence, 734.78 mm Hg is the local atmospheric pressure in mm Hg.
