Barometric formula: Difference between revisions

Latest revision as of 05:55, 29 June 2025

Template:Short description Template:Broader

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

Model equations

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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 km altitude. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non null temperature gradient of $L_{M, b}$ : Script error: No such module "anchor". $P = P_{b} \cdot {[\frac{T_{M, b}}{T_{M, b} + L_{M, b} \cdot (H - H_{b})}]}^{\frac{g_{0^{'}} \cdot M_{0}}{R^{*} \cdot L_{M, b}}}$ .^[1]Template:Rp

The second equation is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude (zero temperature gradient): Script error: No such module "anchor". $P = P_{b} \cdot \exp [\frac{- g_{0^{'}} \cdot M_{0} (H - H_{b})}{R^{*} \cdot T_{M, b}}]$ ,^[1]Template:Rp where:

$P_{b}$ = reference pressure
$T_{M, b}$ = reference temperature (K)
$L_{M, b}$ = temperature gradient (K/m), e.g. -6.5 K/km at sea level. This is the lapse rate with the opposite sign convention.
$H$ = geopotential height at which pressure is calculated (m)
$H_{b}$ = geopotential height of reference level b (meters; e.g., H_b = 11 000 m)
$R^{*}$ = universal gas constant: 8.31432 N·m/(kmol·K)^[1]Template:Rp
$g_{0^{'}}$ = The gravitational acceleration in units of geopotential height, 9.80665 m/s²^[1]Template:Rp
$M_{0}$ = mean molecular weight of air at sea level: 28.9644 kg/kmol^[1]Template:Rp

Or converted to imperial units:^[2]

$P_{b}$ = reference pressure
$T_{M, b}$ = reference temperature (K)
$L_{M, b}$ = temperature gradient (K/ft)
$H$ = height at which pressure is calculated (ft)
$H_{b}$ = height of reference level b (feet; e.g., H_b = 36,089 ft)
$R^{*}$ = universal gas constant; using feet, kelvins, and (SI) moles: Template:Val
$g_{0}$ = gravitational acceleration: 32.17405 ft/s²
$M$ = molar mass of Earth's air: 28.9644 lb/lb-mol

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 R^* are in accordance with the U.S. Standard Atmosphere, 1976, and the value for R^* in particular does not agree with standard values for this constant.^[1]Template:Rp The reference value for P_b for b = 0 is the defined sea level value, P₀ = 101 325 Pa 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 H = H_b+1.^[1]Template:Rp

Subscript b	Geopotential height above MSL (H)^[1]Template:Rp		Static pressure		Standard temperature (K)	Temperature gradient^[1]Template:Rp		Exponent g0 M / R L
Subscript b	(km)	(ft)	(Pa)	(inHg)	Standard temperature (K)	(K/km)	(K/ft)	Exponent g0 M / R L
0	0	0	101 325	29.9213	288.15	-6.5	-0.0019812	-5.25588
1	11	36 089	22 632.1	6.68324	216.65	0.0	0.0	—
2	20	65 617	5 474.89	1.616734	216.65	1.0	0.0003048	34.1626
3	32	104 987	868.019	0.256326	228.65	2.8	0.00085344	12.2009
4	47	154 199	110.9063	0.0327506	270.65	0.0	0.0	—
5	51	167 323	66.9389	0.0197670	270.65	-2.8	-0.00085344	-12.2009
6	71	232 940	3.95642	0.00116833	214.65	-2	-0.0006096	-17.0813

Density can be calculated from pressure and temperature using

$ρ = \frac{P \cdot M_{0}}{R^{*} \cdot T_{M}} = \frac{P \cdot M}{R^{*} \cdot T}$ ,^[1]Template:Rp where

$M_{0}$ is the molecular weight at sea level
$M$ is the mean molecular weight at the altitude of interest
$T$ is the temperature at the altitude of interest
$T_{M} = T \cdot \frac{M_{0}}{M}$ is the molecular-scale temperature.^[1]Template:Rp

The atmosphere is assumed to be fully mixed up to about 80 km, so $M = M_{0}$ within the region of validity of the equations presented here.^[1]Template:Rp

Alternatively, density equations can be derived in the same form as those for pressure, using reference densities instead of reference pressures.Script error: No such module "Unsubst".

This model, with its simple linearly segmented temperature profile, does not closely agree with the physically observed atmosphere at altitudes below 20 km. From 51 km to 81 km it is closer to observed conditions.^[1]Template:Rp

Derivation

The barometric formula can be derived using the ideal gas law: $P = \frac{ρ}{M} R^{*} T$

Assuming that all pressure is hydrostatic: $d P = - ρ g d z$ and dividing this equation by $P$ we get: $\frac{d P}{P} = - \frac{M g d z}{R^{*} T}$

Integrating this expression from the surface to the altitude z we get: $P = P_{0} e^{- \int_{0}^{z} M g d z / R^{*} T}$

Assuming linear temperature change $T = T_{0} - L z$ and constant molar mass and gravitational acceleration, we get the first barometric formula: $P = P_{0} \cdot {[\frac{T}{T_{0}}]}^{\frac{M g}{R^{*} L}}$

Instead, assuming constant temperature, integrating gives the second barometric formula: $P = P_{0} e^{- M g z / R^{*} T}$

In this formulation, R^* is the gas constant, and the term R^*T/Mg gives the scale height (approximately equal to 8.4 km for the troposphere).

(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.)

References

↑ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m Template:Cite report
↑ Mechtly, E. A., 1973: The International System of Units, Physical Constants and Conversion Factors. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C.

[USSA1976-1] ↑ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m Template:Cite report

[conversion-2] Mechtly, E. A., 1973: The International System of Units, Physical Constants and Conversion Factors. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C.

[1]

[2]

@@ Line 4: / Line 4: @@
 The '''barometric formula''' is a [[formula]] used to model how the [[air pressure]] (or [[air density]]) changes with [[altitude]].
-== Pressure equations ==
+== Model equations ==
 {{see also|Atmospheric pressure}}
 [[File:Pressure air.svg|thumb|300px|Pressure as a function of the height above the sea level]]
-There are two equations for computing pressure as a function of height. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non null [[lapse rate]] of <math>L_b</math>:
+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 null temperature gradient of <math>L_{M,b}</math>:
 {{anchor|Non-zero lapse rate}}
-<math display="block">P = P_{b} \left[ 1 - \frac{L_{M,b}}{T_{M,b}} (h - h_{b})\right]^{\frac{g_{0}' M_{0}}{R^{*} L_{M,b}}}</math>
+<math display="block">P = P_{b} \cdot \left[ \frac{ T_{M,b} }{ T_{M,b} + L_{M,b} \cdot \left(H - H_{b}\right) }\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{{cn|date=August 2023}} with altitude ([[lapse rate]] is null):
+.<ref name="USSA1976">{{cite report |author=<!-- not stated --> |date=October 1976 |title=U.S. Standard Atmosphere, 1976 |url=https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf |location=Washington, D.C. |publisher=U.S. Government Printing Office |id=NTRS 19770009539 |access-date=2025-06-29}}</ref>{{rp|p=12}}
+The second equation is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude (zero temperature gradient):
 {{anchor|Zero lapse rate}}
-<math display="block">P = P_b \exp \left[\frac{-g_0 M \left(h-h_b\right)}{R^* {T_{M,b}}}\right]</math>
+<math display="block">P = P_b \cdot \exp \left[\frac{-g_{0}' \cdot M_{0} \left(H-H_b\right)}{R^* \cdot T_{M,b}}\right]</math>
-where:
+,<ref name="USSA1976"/>{{rp|p=12}} where:
 *<math>P_b</math> = reference pressure
 *<math>T_{M,b}</math> = reference temperature ([[kelvin|K]])
-*<math>L_{M,b}</math> = temperature lapse rate (K/m) in [[International Standard Atmosphere|ISA]]
+*<math>L_{M,b}</math> = temperature gradient (K/m), e.g. -6.5&nbsp;K/km at sea level. This is the [[lapse rate]] with the opposite sign convention.
-*<math>h</math> = [[geopotential height]] at which pressure is calculated (m)
+*<math>H</math> = [[geopotential height]] at which pressure is calculated (m)
-*<math>h_b</math> = geopotential height of reference level ''b'' (meters; e.g., ''h<sub>b</sub>'' = 11 000&nbsp;m)
+*<math>H_b</math> = geopotential height of reference level ''b'' (meters; e.g., ''H<sub>b</sub>'' = 11 000&nbsp;m)
-*<math>R^*</math> = [[universal gas constant]]: 8.3144598&nbsp;J/(mol·K)
+*<math>R^*</math> = [[universal gas constant]]: 8.31432&nbsp;N·m/(kmol·K)<ref name="USSA1976"/>{{rp|p=3}}
-*<math>g_0</math> = [[standard gravity|gravitational acceleration]]: 9.80665&nbsp;m/s<sup>2</sup>
+*<math>g_{0}'</math> = The [[standard gravity|gravitational acceleration]] in units of geopotential height, 9.80665&nbsp;m/s<sup>2</sup><ref name="USSA1976"/>{{rp|p=3}}
-*<math>M</math> = molar mass of Earth's air: 0.0289644&nbsp;kg/mol
+*<math>M_{0}</math> = mean molecular weight of air at sea level: 28.9644&nbsp;kg/kmol<ref name="USSA1976"/>{{rp|p=9}}
 Or converted to [[imperial units]]:<ref name="conversion">Mechtly, E. A., 1973: ''[https://ntrs.nasa.gov/api/citations/19730018242/downloads/19730018242.pdf The International System of Units, Physical Constants and Conversion Factors]''.  NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C.</ref>
@@ Line 27: / Line 29: @@
 *<math>P_b</math> = reference pressure
 *<math>T_{M,b}</math> = reference temperature ([[kelvin|K]])
-*<math>L_{M,b}</math> = temperature lapse rate (K/ft) in [[International Standard Atmosphere|ISA]]
+*<math>L_{M,b}</math> = temperature gradient (K/ft)
-*<math>h</math> = height at which pressure is calculated (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>'' = 36,089&nbsp;ft)
+*<math>H_b</math> = height of reference level ''b'' (feet; e.g., ''H<sub>b</sub>'' = 36,089&nbsp;ft)
 *<math>R^*</math> = [[universal gas constant]]; using feet, kelvins, and (SI) [[mole (unit)|moles]]: {{val|8.9494596e4|u=lb·ft<sup>2</sup>/(lb-mol·K·s<sup>2</sup>)}}
 *<math>g_0</math> = [[standard gravity|gravitational acceleration]]: 32.17405&nbsp;ft/s<sup>2</sup>
 *<math>M</math> = molar mass of Earth's air: 28.9644&nbsp;lb/lb-mol
-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.<ref name="USSA1976">[https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf U.S. Standard Atmosphere], 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is 17 Mb)</ref> The reference value for ''P<sub>b</sub>'' for ''b'' = 0 is the defined sea level value, ''P''<sub>0</sub> = 101 325 [[pascal (unit)|Pa]] or 29.92126 inHg.  Values of ''P<sub>b</sub>'' 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 ''h'' = ''h''<sub>''b''+1</sub>.<ref name=USSA1976/>
+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.<ref name="USSA1976"/>{{rp|p=3}} The reference value for ''P<sub>b</sub>'' for ''b'' = 0 is the defined sea level value, ''P''<sub>0</sub> = 101 325 [[pascal (unit)|Pa]] or 29.92126 inHg.  Values of ''P<sub>b</sub>'' 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 ''H'' = ''H''<sub>''b''+1</sub>.<ref name=USSA1976/>{{rp|p=12}}
 {| class="wikitable" style="text-align: center"
@@ Line 41: / Line 43: @@
 ! colspan="2"|Geopotential
 height above MSL
-(h)
+(H)<ref name="USSA1976" />{{rp|p=3}}
 ! colspan="2"|Static pressure
 ! rowspan="2"|Standard temperature<br> (K)
-! colspan="2"|Temperature lapse rate
+! colspan="2"|Temperature gradient<ref name="USSA1976" />{{rp|p=3}}
 ! rowspan="2"|Exponent <br> g0 M / R L
 |-
-! (m) !! (ft)!! (Pa) !! (inHg) !! (K/m) !! (K/ft)
+! (km) !! (ft)!! (Pa) !! (inHg) !! (K/km) !! (K/ft)
 |-
-| 0 || 0 || 0 || 101 325.00 || 29.92126 || 288.15 || 0.0065 || 0.0019812 || 5.25588
+| 0 || 0 || 0 || 101 325 || 29.9213 || 288.15 || -6.5 || -0.0019812 || -5.25588
 |-
-| 1 || 11 000 || 36,089 || 22 632.10 || 6.683245 || 216.65 || 0.0 || 0.0 || &mdash;
+| 1 || 11 || 36 089 || 22 632.1 || 6.68324 || 216.65 || 0.0 || 0.0 || &mdash;
 |-
-| 2 || 20 000 || 65,617 || 5474.89 || 1.616734 || 216.65 || -0.001 || -0.0003048 || -34.1626
+| 2 || 20 || 65 617 || 5 474.89 || 1.616734 || 216.65 || 1.0 || 0.0003048 || 34.1626
 |-
-| 3 || 32 000 || 104,987 || 868.02 || 0.2563258 || 228.65 || -0.0028 || -0.00085344 || -12.2009
+| 3 || 32 || 104 987 || 868.019 || 0.256326 || 228.65 || 2.8 || 0.00085344 || 12.2009
 |-
-| 4 || 47 000 || 154,199 || 110.91 || 0.0327506 || 270.65 || 0.0 || 0.0 || &mdash;
+| 4 || 47 || 154 199 || 110.9063 || 0.0327506 || 270.65 || 0.0 || 0.0 || &mdash;
 |-
-| 5 || 51 000 || 167,323 || 66.94 || 0.01976704 || 270.65 || 0.0028 || 0.00085344 || 12.2009
+| 5 || 51 || 167 323 || 66.9389 || 0.0197670 || 270.65 || -2.8 || -0.00085344 || -12.2009
 |-
-| 6 || 71 000 || 232,940 || 3.96 || 0.00116833 || 214.65 || 0.002 || 0.0006096 || 17.0813
+| 6 || 71 || 232 940 || 3.95642 || 0.00116833 || 214.65 || -2 || -0.0006096 || -17.0813
 |}
-==Density equations==
+Density can be calculated from pressure and temperature using
-{{further|Atmospheric density}}
-The expressions for calculating density are nearly identical to calculating pressure.  The only difference is the exponent in Equation 1.
-There are two equations for computing density as a function of height. The first equation is applicable to the standard model of the [[troposphere]] in which the temperature is assumed to vary with altitude at a [[lapse rate]] of <math>L_b</math>; the second equation is applicable to the standard model of the [[stratosphere]] in which the temperature is assumed not to vary with altitude.
-Equation 1:
-<math display="block">\rho = \rho_b \left[\frac{T_b - (h-h_b) L_b}{T_b}\right]^{\left(\frac{g_0 M}{R^*  L_b}-1\right)}</math>
-which is equivalent to the ratio of the relative pressure and temperature changes
-<math display="block">\rho = \rho_b \frac{P}{T} \frac{T_b}{P_b} </math>
-Equation 2:
+<math>\rho = \frac{ P \cdot M_{0} }{ R^* \cdot T_{M} } = \frac{ P \cdot M }{ R^* \cdot T }</math>
-<math display="block">\rho =\rho_b \exp\left[\frac{-g_0 M \left(h-h_b\right)}{R^* T_b}\right]</math>
+,<ref name="USSA1976" />{{rp|p=15}} where
-where
+* <math>M_{0}</math> is the molecular weight at sea level
-*<math>{\rho}</math> = mass density (kg/m<sup>3</sup>)
+* <math>M</math> is the mean molecular weight at the altitude of interest
-*<math>T_b</math> = standard temperature (K)
+* <math>T</math> is the temperature at the altitude of interest
-*<math>L</math> = standard temperature lapse rate (see table below) (K/m) in [[International Standard Atmosphere|ISA]]
+* <math>T_{M} = T \cdot \frac {M_0}{M}</math> is the molecular-scale temperature.<ref name="USSA1976" />{{rp|p=9}}
-*<math>h</math> = height above sea level (geopotential meters)
-*<math>R^*</math> = [[universal gas constant]] 8.3144598&nbsp;N·m/(mol·K)
-*<math>g_0</math> = gravitational acceleration: 9.80665&nbsp;m/s<sup>2</sup>
-*<math>M</math> = molar mass of Earth's air: 0.0289644&nbsp;kg/mol
-or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.):<ref name="conversion"/>
+The atmosphere is assumed to be fully mixed up to about 80&nbsp;km, so <math>M = M_{0}</math> within the region of validity of the equations presented here.<ref name="USSA1976" />{{rp|p=9}}
-*<math>{\rho}</math> = mass density ([[slug (unit)|slug]]/ft<sup>3</sup>)
-*<math>{T_b}</math> = standard temperature (K)
-*<math>{L}</math> = standard temperature lapse rate (K/ft)
-*<math>{h}</math> = height above sea level (geopotential feet)
-*<math>{R^*}</math> = universal gas constant: 8.9494596×10<sup>4</sup>&nbsp;ft<sup>2</sup>/(s·K)
-*<math>{g_0}</math> = gravitational acceleration: 32.17405&nbsp;ft/s<sup>2</sup>
-*<math>{M}</math> = molar mass of Earth's air: 28.9644&nbsp;lb/lb-mol
-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. The reference value for ''ρ<sub>b</sub>'' for ''b'' = 0 is the defined sea level value, ''ρ''<sub>0</sub> = 1.2250&nbsp;kg/m<sup>3</sup> or 0.0023768908&nbsp;slug/ft<sup>3</sup>. Values of ''ρ<sub>b</sub>'' 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 ''h'' = ''h''<sub>''b''+1</sub>.<ref name=USSA1976/>
+Alternatively, density equations can be derived in the same form as those for pressure, using reference densities instead of reference pressures.{{citation needed|date=June 2025}}
-In these equations, ''g''<sub>0</sub>, ''M'' and ''R''<sup>*</sup> are each single-valued constants, while ''ρ'', ''L'', ''T'' and ''h'' are multi-valued 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 that the value for ''R''<sup>*</sup> in particular does not agree with standard values for this constant.<ref name="USSA1976"/>
+This model, with its simple linearly segmented temperature profile, does not closely agree with the physically observed atmosphere at altitudes below 20&nbsp;km. From 51&nbsp;km to 81&nbsp;km it is closer to observed conditions.<ref name="USSA1976" />{{rp|p=1}}
-{| class="wikitable"
-|-
-! rowspan="2"|Subscript ''b''
-! colspan="2"|Geopotential
-height above MSL
-(h)
-! colspan="2"|Mass Density (<math>\rho</math>)
-! rowspan="2"|Standard Temperature (''T''')<br> (K)
-! colspan="2"|Temperature Lapse Rate (''L'')
-|-
-! (m) !! (ft)!! (kg/m<sup>3</sup>) !! (slug/ft<sup>3</sup>) !! (K/m) !! (K/ft)
-|-
-| align="center" |0
-| align="center" |0
-| align="center" |0
-| align="center" |1.2250
-| align="center" |{{val|2.3768908|e=-3}}
-| align="center" |288.15
-| align="center" |0.0065
-| align="center" |0.0019812
-|-
-| align="center" |1
-| align="center" |11 000
-| align="center" |36,089.24
-| align="center" |0.36391
-| align="center" |{{val|7.0611703|e=-4}}
-| align="center" |216.65
-| align="center" |0.0
-| align="center" |0.0
-|-
-| align="center" |2
-| align="center" |20 000
-| align="center" |65,616.79
-| align="center" |0.08803
-| align="center" |{{val|1.7081572|e=-4}}
-| align="center" |216.65
-| align="center" |-0.001
-| align="center" |-0.0003048
-|-
-| align="center" |3
-| align="center" |32 000
-| align="center" |104,986.87
-| align="center" |0.01322
-| align="center" |{{val|2.5660735|e=-5}}
-| align="center" |228.65
-| align="center" |-0.0028
-| align="center" |-0.00085344
-|-
-| align="center" |4
-| align="center" |47 000
-| align="center" |154,199.48
-| align="center" |0.00143
-| align="center" |{{val|2.7698702|e=-6}}
-| align="center" |270.65
-| align="center" |0.0
-| align="center" |0.0
-|-
-| align="center" |5
-| align="center" |51 000
-| align="center" |167,322.83
-| align="center" |0.00086
-| align="center" |{{val|1.6717895|e=-6}}
-| align="center" |270.65
-| align="center" |0.0028
-| align="center" |0.00085344
-|-
-| align="center" |6
-| align="center" |71 000
-| align="center" |232,939.63
-| align="center" |0.000064
-| align="center" |{{val|1.2458989|e=-7}}
-| align="center" |214.65
-| align="center" |0.002
-| align="center" |0.0006096
-|}
 ==Derivation==

Barometric formula: Difference between revisions

Latest revision as of 05:55, 29 June 2025

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Model equations

Derivation

See also

References

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Barometric formula: Difference between revisions

Latest revision as of 05:55, 29 June 2025

Model equations

Derivation

See also

References

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