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Hypsometric Equation

The hypsometric equation, also known as the thickness equation, relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer under the assumptions of constant temperature and gravity.

The final pressure equals the reference pressure times an exponential that decreases as the difference between the altitudes of the final and reference pressures divided by the reference temperature grows.

Formula

QuantityVariable[Subscript["P", "2"], "Pressure"] == E^((Quantity[-0.0034842841364027557, ("Kelvins"*"Kilograms"*"StandardAccelerationOfGravity")/"Joules"]*(QuantityVariable[Subscript["H", "2"], "Height"] - QuantityVariable[Subscript["H", "r"], "Height"]))/QuantityVariable[Subscript["T", "r"], "Temperature"])*QuantityVariable[Subscript["P", "r"], "Pressure"]

symbol description physical quantity
P2 final pressure "Pressure"
H2 altitude "Height"
Hr reference altitude "Height"
Tr reference temperature "Temperature"
Pr reference pressure "Pressure"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Hypsometric Equation"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Hypsometric Equation"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject["Hypsometric Equation"], {QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("2"\)]\),"Pressure"] -> Quantity[1, "Atmospheres"], QuantityVariable[ \!\(\*SubscriptBox[\("H"\), \("r"\)]\),"Height"] -> Quantity[5, "Kilometers"], QuantityVariable[ \!\(\*SubscriptBox[\("H"\), \("2"\)]\),"Height"] -> Quantity[20, "Kilometers"]}]
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