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Upper Atmosphere
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Calculation of the relationship between atmospheric pressure and altitude for dry air

parameters and units:

z [m] = altitude

p0 [hPa] = pressure at the ground

p [hPa] = pressure at altitude z

R* = 287 J kg-1 K-1 = gas constant for dry air

R* = R / Ma

R = gas constant = 8.314 J K-1 mol-1

Ma = molecular weight of air = 28.96 g mol-1

 

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g = gravity accelaration constant
= 9.81 m s-2

Tm [K] = mid temperature between the the temperature at the ground T0 and the temperature in altitude z Tz

Tm = (T0 + Tz) / 2

g / R* = 0.034 K m-1

 

1 J = 1 N m

1 N = 1 kg m s-2

 

pressure and altitude

pressure and temperature versus altitude

Relationship between pressure temperature and altitude. Full size: 90 K

The formula is only valid for dry air. For humid air the molecular weight changes.
For the plotted graph the following reasonable assumptions have been made:

Temperature at the ground: 20C
Temperature decrease rate: - 1C / 200 m
Temperature at 10000 m: - 30C

Pressure at the ground: 1000 hPa

It can be seen from the calculated pressures in higher altitudes, that the pressure in 5,500 m is about 500 hPa in 11,000 m about 250 hPa.

 

about this page:
author: Dr. Elmar Uherek - Max Planck Institute, Mainz
last published: 2004-04-20

 

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last updated 22.07.2004 16:44:22 | © ESPERE-ENC 2003 - 2013