Tuesday, March 17, 2009

Pressure and thickness

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The average atmospheric pressure, at sea level, is about 101.3 kilopascals (14.69 psi); total atmospheric mass is 5.1480×1018 kg (1.135×1019 lb).

Atmospheric pressure is a direct result of the total weight of the air above the point at which the pressure is measured. Air pressure varies with location and time, because the amount (and weight) of air above the earth varies with location and time. However, the average mass of the air above a square meter of the Earth's surface can be calculated from the total amount of air and the surface area of the Earth. The total air mass is 5148.0 teratonnes and area is 51007.2 megahectares. Thus 5148.0/510.072 = 10.093 tonnes (9.934 LT; 11.126 ST) per square meter or 14.356 pounds per square inch (98.98 kPa). This is about 2.5% below the officially standardized unit atmosphere (1 atm) of 101.325 kPa or 14.696 psi, and corresponds to the mean pressure not at sea level, but at the mean base of the atmosphere as contoured by the Earth's terrain.

Were atmospheric density to remain constant with height the atmosphere would terminate abruptly at 7.81 km (25,600 ft). Instead, density decreases with height, dropping by 50% at an altitude of about 5.6 km (18,000 ft). For comparison the highest mountain, Mount Everest, is higher, at 8.8 km (29,000 ft), so air is less than half as dense at the summit than at sea level. This is why it is so difficult to climb without supplemental oxygen.

This pressure drop is approximately exponential, so that pressure decreases by approximately half every 5.6 km (18,000 ft) and by 63.2% (1 − 1 / e = 1 − 0.368 = 0.632) every 7.64 km (25,100 ft), the average scale height of Earth's atmosphere below 70 km (43 mi; 230,000 ft). However, because of changes in temperature, average molecular weight, and gravity throughout the atmospheric column, the dependence of atmospheric pressure on altitude is modeled by separate equations for each of the layers listed above. Even in the exosphere, the atmosphere is still present. This can be seen by the effects of atmospheric drag on satellites.

In summary, the equations of pressure by altitude in the above references can be used directly to estimate atmospheric thickness. However, the following published data are given for reference:[4]

  • 50% of the atmosphere by mass is below an altitude of 5.6 km (18,000 ft).
  • 90% of the atmosphere by mass is below an altitude of 16 km (52,000 ft). The common altitude of commercial airliners is about 10 km (33,000 ft) and Mt. Everest's summit is 8,848 m (29,030 ft) above sea level.
  • 99.99997% of the atmosphere by mass is below 100 km (62 mi; 330,000 ft), although in the rarefied region above this there are auroras and other atmospheric effects. The highest X-15 plane flight in 1963 reached an altitude of 354,300 ft (108.0 km).

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