Aerostatics

Treatment of the equations of gaseous behaviour at rest is generally taken, as in hydrostatics, to begin with a consideration of the general equations of momentum for fluid flow, which can be expressed as:

${\displaystyle \rho [{\partial U_{j} \over \partial t}+U_{i}{\partial U_{j} \over \partial t}]=-{\partial P \over \partial x_{j}}-{\partial \tau _{ij} \over \partial x_{i}}+\rho g_{j}}$,

where ${\displaystyle \rho }$ is the mass density of the fluid, ${\displaystyle U_{j}}$ is the instantaneous velocity, ${\displaystyle P}$ is fluid pressure, ${\displaystyle g}$ are the external body forces acting on the fluid, and ${\displaystyle \tau _{ij}}$ is the momentum transport coefficient. As the fluid's static nature mandates that ${\displaystyle U_{j}=0}$, and that ${\displaystyle \tau _{ij}=0}$, the following set of partial differential equations representing the basic equations of aerostatics is found.[1]^:154

${\displaystyle {\partial P \over \partial x_{j}}=\rho g_{j}}$

However, the presence of a non-constant density as is found in gaseous fluid systems (due to the compressibility of gases) requires the inclusion of the ideal gas law:

${\displaystyle {P \over \rho }=RT}$,

where ${\displaystyle R}$ denotes the universal gas constant, and ${\displaystyle T}$ the temperature of the gas, in order to render the valid aerostatic partial differential equations:

${\displaystyle {\partial P \over \partial x_{j}}=\rho {\hat {g_{j}}}={P \over \ RT}{\hat {g_{j}}}}$,

which can be employed to compute the pressure distribution in gases whose thermodynamic states are given by the equation of state for ideal gases.[1]^:183

• Atmospheric pressure fluctuation
• Composition of mountain air
• Cross-section of the atmosphere
• Gas density
• Gas diffusion in soil
• Gas pressure
• Kinetic theory of gases
• Partial pressures in gas mixtures
• Pressure measurement

• Aeronautics