Density Scale Height -- from Eric Weisstein's World of Physics

Fluid Mechanics "> Buoyancy and Hydrostatics v

Density Scale Height

For an ideal gas,

where P is the pressure, R is the universal gas constant, T is the temperature, and is the molar mass. Taking the derivative with respect to vertical distance z and using the hydrostatic law gives

where is the gas density and g is the gravitational acceleration. Rearranging,

so

where the density scale height is defined as

Pressure Scale Height, Scale Height