The barometric formula is a formula used to model how the air pressure (or air density) changes with altitude.

Model equations

thumb|upright=1.2|Pressure as a function of the height above the sea level

The U.S. Standard Atmosphere gives two equations for computing pressure as a function of height, valid from sea level to 86&nbsp;km altitude. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non-zero temperature gradient of <math>L_{M,b}</math>:

<math display="block">

P = P_b \cdot \left[ \frac{ T_{M,b} }{ T_{M,b} + L_{M,b} \cdot (H - H_{b}) }\right]^{\frac{g_0' \cdot M_0}{R^* \cdot L_{M,b}.

</math>

The second equation is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude (zero temperature gradient):

: <math>P_b</math> = reference pressure;

: <math>T_{M,b}</math> = reference temperature (K);

: <math>L_{M,b}</math> = temperature gradient (K/ft);

: <math>H</math> = height at which pressure is calculated (ft);

: <math>H_b</math> = height of reference level b (feet, e.g., H<sub>b</sub> = );

: <math>R^*</math> = universal gas constant, using feet, kelvins, and (SI) moles, taken to be roughly &nbsp; by correctly converting the (incorrectly) taken constant from metric to imperial;

: <math>g_0</math> = gravitational acceleration = ;

: <math>M</math> = mean molar mass of Earth's air = (both lbs are pound-mass, not pound-force).

The value of subscript b ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In these equations, g<sub>0</sub>, M and R<sup>*</sup> are each single-valued constants, while P, L, T, and H are multivalued constants in accordance with the table below. The values used for M, g<sub>0</sub>, and R<sup>*</sup> are in accordance with the U.S. Standard Atmosphere, 1976, and the value for R<sup>*</sup> in particular does not agree with standard values for this constant.

(For exact results, it should be remembered that atmospheres containing water do not behave as an ideal gas. See real gas or perfect gas or gas for further understanding.)

Barosphere<span class="anchor" id="Barosphere"></span>

The barosphere is the region of a planetary atmosphere where the barometric law applies. It ranges from the ground to the thermopause, also known as the baropause. Above this altitude is the exosphere, where the atmospheric velocity distribution is non-Maxwellian due to high velocity atoms and molecules being able to escape the atmosphere.

See also

  • Hypsometric equation
  • NRLMSISE-00

References