Barometric Formula - Pressure Equations

Pressure Equations

There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of Standard Temperature Lapse Rate is not equal to zero; the second equation is used when standard temperature lapse rate equals zero.

Equation 1:

Equation 2:

where

= Static pressure (pascals)

= Standard temperature (K)

= Standard temperature lapse rate -0.0065 (K/m) in ISA

= Height above sea level (meters)

= Height at bottom of layer b (meters; e.g., = 11,000 meters)

= Universal gas constant for air: 8.31432 N·m /(mol·K)

= Gravitational acceleration (9.80665 m/s2)

= Molar mass of Earth's air (0.0289644 kg/mol)

Or converted to Imperial units:

where

= Static pressure (inches of mercury, inHg)

= Standard temperature (K)

= Standard temperature lapse rate (K/ft)

= Height above sea level (ft)

= Height at bottom of layer b (feet; e.g., = 36,089 ft)

= Universal gas constant; using feet, kelvins, and (SI) moles: 8.9494596×104 lb·ft2/(lbmol·K·s2)

= Gravitational acceleration (32.17405 ft/s2)

= Molar mass of Earth's air (28.9644 lb/lbmol)

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, g₀, M and R* 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, g₀, and are in accordance with the U.S. Standard Atmosphere, 1976, and the value for in particular does not agree with standard values for this constant. The reference value for P_b for b = 0 is the defined sea level value, P₀ = 101325 pascals or 29.92126 inHg. Values of P_b of b = 1 through b = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when .: