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Barometric Formula for Density

The barometric formula (also called the exponential atmosphere or isothermal atmosphere) is a formula used to model how the density of the air changes with altitude.

The density at altitude depends on the density at the surface and an exponential factor that decreases with altitude, gravitational acceleration and the molar mass of the atmosphere. The factor also declines more slowly with increased temperature.

Formula

QuantityVariable["ρ", "MassDensity"] == E^((Quantity[-1, "MolarGasConstant"^(-1)]*QuantityVariable["g", "GravitationalAcceleration"]*QuantityVariable["h", "Height"]*QuantityVariable["M", "MolarMass"])/QuantityVariable["T", "Temperature"])*QuantityVariable[Subscript["ρ", "0"], "MassDensity"]

Forms

Examples

Get the resource:

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ResourceObject["Barometric Formula for Density"]
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Get the formula:

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FormulaData[ResourceObject["Barometric Formula for Density"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Barometric Formula for Density"], {QuantityVariable[ "g","GravitationalAcceleration"] -> Quantity[1, "StandardAccelerationOfGravity"], QuantityVariable["T","Temperature"] -> Quantity[300, "Kelvins"], QuantityVariable["\[Rho]","MassDensity"] -> Quantity[1.3`, ("Kilograms")/("Meters")^3], QuantityVariable["h","Height"] -> Quantity[1, "Kilometers"], QuantityVariable["M","MolarMass"] -> Quantity[29, ("Grams")/("Moles")]}]
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